<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">a</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K2">COMPLEX</a> ;<br/><b>let </b><font color="Maroon">b</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K2">COMPLEX</a> ;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:67"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>and </b><br/><a NAME="E2:67"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/>

<a NAME="E3:67"/><i><font color="Green">E29</font></i>: 
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="ref" href="complex2.html#T21" target="_self">Th21</a>, <a class="ref" href="complex1.html#T131">COMPLEX1:131</a></i>;<br/>
<a NAME="E4:67"/><i><font color="Green">E30</font></i>: 
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="ref" href="complex2.html#T22" target="_self">Th22</a>, <a class="ref" href="complex1.html#T131">COMPLEX1:131</a></i>;<br/>
<b>set </b><font color="Maroon">mab</font> = <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span>;<br/>
<b>set </b><font color="Maroon">mabi</font> = <span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> ;<br/>
<a NAME="E5:67"/><i><font color="Green">E31</font></i>: 
( <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp; <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 )
 
<b>by </b><i><a class="ref" href="complex1.html#T132">COMPLEX1:132</a></i>;<br/>
<a NAME="E6:67"/><b>then </b>
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 <a href="real_1.html#K4">*</a> <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span>
 
<b>by </b><i><a class="ref" href="complex2.html#T23" target="_self">Th23</a>, <a class="ref" href="complex2.html#T24" target="_self">Th24</a>, <a class="ref" href="xreal_1.html#T70">XREAL_1:70</a></i>;<br/>
<a NAME="E7:67"/><b>then </b><i><font color="Green">E32</font></i>: 
<span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a>  <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="ref" href="xreal_1.html#T124">XREAL_1:124</a></i>;<br/>
<b>set </b><font color="Maroon">ra</font> =  <a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">a</font>,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">rb</font> =  <a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">r</font> =  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span>;<br/>
<a NAME="E8:67"/><i><font color="Green">E33</font></i>: 
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="complex2.html#T23" target="_self">Th23</a>, <a class="ref" href="complex2.html#T25" target="_self">Th25</a>, <a class="ref" href="complex2.html#T26" target="_self">Th26</a>, <a class="ref" href="xreal_1.html#T70">XREAL_1:70</a></i>;<br/>
<a NAME="E9:67"/><i><font color="Green">E48</font></i>: 
 <a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">a</font>,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">0 <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7">&lt;i&gt;</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="complex1.html#T27">COMPLEX1:27</a>, <a class="ref" href="sin_cos.html#T34">SIN_COS:34</a></i>;<br/>
<a NAME="E10:67"/>
 <a href="complex2.html#K3" target="_self">angle</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="hidden.html#R1">=</a>  <a href="complex2.html#K3" target="_self">angle</a> <span class="p1">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">a</font>,<span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="complex2.html#T21" target="_self">Th21</a>, <a class="ref" href="complex2.html#T22" target="_self">Th22</a>, </i>;<br/>
<a NAME="E11:67"/><b>then </b><i><font color="Green">E49</font></i>: 
 <a href="complex2.html#K3" target="_self">angle</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="hidden.html#R1">=</a>  <a href="complex2.html#K3" target="_self">angle</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">a</font>,<span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p2"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p5"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>,0</span><a href="arytm_0.html#K5">*]</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p2"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p5"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>,0</span><a href="arytm_0.html#K5">*]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="complex2.html#T26" target="_self">Th26</a>, <a class="txt" href="complex2.html#E16"><i><font color="Green">Lemma53</font></i></a></i>;<br/>
<a NAME="E12:67"/><i><font color="Green">E50</font></i>: 
(  <a href="complex1.html#K3">Re</a> <span class="p1">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">a</font>,<span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> &amp;  <a href="complex1.html#K4">Im</a> <span class="p1">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">a</font>,<span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0 )
 
<b>by </b><i><a class="ref" href="complex1.html#T28">COMPLEX1:28</a>, </i>;<br/>
<a NAME="E13:67"/>
<span class="p1"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p4"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>,0</span><a href="arytm_0.html#K5">*]</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">0 <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7">&lt;i&gt;</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="complex1.html#T27">COMPLEX1:27</a></i>;<br/>
<a NAME="E14:67"/><b>then </b><i><font color="Green">E51</font></i>: 
(  <a href="complex1.html#K3">Re</a> <span class="p1"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p4"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>,0</span><a href="arytm_0.html#K5">*]</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a>  &amp;  <a href="complex1.html#K4">Im</a> <span class="p1"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p4"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>,0</span><a href="arytm_0.html#K5">*]</a></span> <a href="hidden.html#R1">=</a> 0 )
 
<b>by </b><i><a class="ref" href="complex1.html#T28">COMPLEX1:28</a></i>;<br/>
<a NAME="E15:67"/><b>then </b>
(  <a href="complex1.html#K3">Re</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">a</font>,<span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p2"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p5"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>,0</span><a href="arytm_0.html#K5">*]</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p4"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default">0 <a href="real_1.html#K4">*</a> 0</span>)</span> &amp;  <a href="complex1.html#K4">Im</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">a</font>,<span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p2"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p5"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>,0</span><a href="arytm_0.html#K5">*]</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> 0</span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default">0 <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p4"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span></span>)</span> )
 
<b>by </b><i>, <a class="ref" href="complex1.html#T24">COMPLEX1:24</a></i>;<br/>
<a NAME="E16:67"/><b>then </b>
<span class="p1">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">a</font>,<span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p1"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p4"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>,0</span><a href="arytm_0.html#K5">*]</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p4"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">0 <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7">&lt;i&gt;</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="complex1.html#T29">COMPLEX1:29</a></i>;<br/>
<a NAME="E17:67"/><b>then </b>
<span class="p1">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">a</font>,<span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p1"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p4"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>,0</span><a href="arytm_0.html#K5">*]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p5"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span></span>)</span>,0</span><a href="arytm_0.html#K5">*]</a></span>
 
<b>by </b><i><a class="ref" href="complex1.html#T27">COMPLEX1:27</a></i>;<br/>
<a NAME="E18:67"/><b>then </b><i><font color="Green">E52</font></i>: 
 <a href="complex2.html#K3" target="_self">angle</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="hidden.html#R1">=</a>  <a href="comptrig.html#K1">Arg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p2"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p5"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>,0</span><a href="arytm_0.html#K5">*]</a></span></span>)</span>
 
<b>by </b><i>, , <a class="txt" href="complex2.html#E14:67"><i><font color="Green">E51</font></i></a></i>;<br/>
<b>set </b><font color="Maroon">IT</font> = <span class="p1">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p1"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p4"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>,0</span><a href="arytm_0.html#K5">*]</a></span>;<br/>
<a NAME="E19:67"/><i><font color="Green">E68</font></i>: 
(  <a href="complex1.html#K3">Re</a> <span class="p1">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">b</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="sin_cos.html#K24">cos</a> <span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">b</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="sin_cos.html#K21">sin</a> <span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span>)</span> &amp;  <a href="complex1.html#K4">Im</a> <span class="p1">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">b</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="sin_cos.html#K21">sin</a> <span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">b</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="sin_cos.html#K24">cos</a> <span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="complex2.html#T11" target="_self">Th11</a></i>;<br/>
<i><font color="Green">E69</font></i>: <span class="p1">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p1"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p4"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>,0</span><a href="arytm_0.html#K5">*]</a></span> = 
<span class="p1"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p0">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p5"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>,0</span><a href="arytm_0.html#K5">*]</a></span></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K24">cos</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p0"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>,0</span><a href="arytm_0.html#K5">*]</a></span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p0">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p5"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>,0</span><a href="arytm_0.html#K5">*]</a></span></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K21">sin</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p0"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>,0</span><a href="arytm_0.html#K5">*]</a></span></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="arytm_0.html#K5">*]</a></span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p5">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p0">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>,0</span><a href="arytm_0.html#K5">*]</a></span></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="sin_cos.html#K24">cos</a> <span class="p3">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p0">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p5"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>,0</span><a href="arytm_0.html#K5">*]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p0">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p5"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>,0</span><a href="arytm_0.html#K5">*]</a></span></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K21">sin</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p0"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>,0</span><a href="arytm_0.html#K5">*]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7">&lt;i&gt;</a> </span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#T27">COMPLEX1:27</a></i>
;<br/>
<i><font color="Green">E70</font></i>:  <a href="complex1.html#K3">Re</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p2"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p5"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>,0</span><a href="arytm_0.html#K5">*]</a></span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p3">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p4"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p3">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="complex2.html#T27" target="_self">Th27</a>, <a class="ref" href="complex1.html#T24">COMPLEX1:24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p2">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>

;<br/>
<i><font color="Green">E120</font></i>:  <a href="complex1.html#K4">Im</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p2"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p5"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>,0</span><a href="arytm_0.html#K5">*]</a></span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p3">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> 0</span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p3">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p4"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="complex2.html#T27" target="_self">Th27</a>, <a class="ref" href="complex1.html#T24">COMPLEX1:24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p2">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>

;<br/>
<font color="Maroon">a</font> = 
<span class="p1"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K24">cos</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K21">sin</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span><a href="arytm_0.html#K5">*]</a></span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="sin_cos.html#K24">cos</a> <span class="p3">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K21">sin</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7">&lt;i&gt;</a> </span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#T27">COMPLEX1:27</a></i>
;<br/>
<a NAME="E24:67"/><b>then </b>
(  <a href="complex1.html#K3">Re</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K24">cos</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span> &amp;  <a href="complex1.html#K4">Im</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K21">sin</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="complex1.html#T28">COMPLEX1:28</a></i>;<br/>
<a NAME="E25:67"/><b>then </b><i><font color="Green">E121</font></i>: 
(  <a href="sin_cos.html#K24">cos</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> &amp;  <a href="sin_cos.html#K21">sin</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> )
 
<b>by </b><i><a class="ref" href="complex2.html#T23" target="_self">Th23</a>, <a class="ref" href="xcmplx_1.html#T90">XCMPLX_1:90</a></i>;<br/>
<i><font color="Green">E122</font></i>: <font color="Maroon">a</font> <a href="complex2.html#K1" target="_self">.|.</a> <font color="Maroon">b</font> = 
<span class="p1"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span></span><a href="arytm_0.html#K5">*]</a></span>
<b>by </b><i><a class="txt" href="complex2.html#E3:67"><i><font color="Green">E29</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7">&lt;i&gt;</a> </span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#T27">COMPLEX1:27</a></i>
;<br/>
<a NAME="E27:67"/><b>then </b><i><font color="Green">E123</font></i>: 
 <a href="complex1.html#K3">Re</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="complex2.html#K1" target="_self">.|.</a> <font color="Maroon">b</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">b</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="complex1.html#T28">COMPLEX1:28</a></i>;<br/>
<i><font color="Green">E124</font></i>:  <a href="complex1.html#K3">Re</a> <span class="p1">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">b</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="sin_cos.html#K24">cos</a> <span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">b</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K21">sin</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="complex2.html#E20:67"><i><font color="Green">E69</font></i></a>, <a class="ref" href="sin_cos.html#T34">SIN_COS:34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">b</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="sin_cos.html#K24">cos</a> <span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">b</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="sin_cos.html#K21">sin</a> <span class="p3">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">b</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">b</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="complex2.html#T36" target="_self">Th36</a>, <a class="ref" href="sin_cos.html#T34">SIN_COS:34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">b</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">b</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T75">XCMPLX_1:75</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">b</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">b</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T75">XCMPLX_1:75</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="complex2.html#K1" target="_self">.|.</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span>
<b>by </b><i><a class="ref" href="complex2.html#T38" target="_self">Th38</a>, <a class="ref" href="xcmplx_1.html#T63">XCMPLX_1:63</a></i>
;<br/>
<i><font color="Green">E125</font></i>:  <a href="complex1.html#K4">Im</a> <span class="p1">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">b</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K21">sin</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">b</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="sin_cos.html#K24">cos</a> <span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="complex2.html#E20:67"><i><font color="Green">E69</font></i></a>, <a class="ref" href="sin_cos.html#T34">SIN_COS:34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">b</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="complex2.html#T36" target="_self">Th36</a>, <a class="ref" href="sin_cos.html#T34">SIN_COS:34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">b</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T75">XCMPLX_1:75</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">b</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T75">XCMPLX_1:75</a></i>
<br/>.= 
 <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p0">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">b</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T63">XCMPLX_1:63</a></i>
<br/>.= 
 <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p0">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">b</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T188">XCMPLX_1:188</a></i>
<br/>.= 
 <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="complex2.html#K1" target="_self">.|.</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span></span>)</span>
<b>by </b><i><a class="ref" href="complex2.html#T37" target="_self">Th37</a>, <a class="ref" href="complex1.html#T28">COMPLEX1:28</a></i>
;<br/>
<a NAME="E30:67"/><i><font color="Green">E126</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span> <a href="square_1.html#K5">^2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i><a class="ref" href="xreal_1.html#T65">XREAL_1:65</a></i>;<br/>
<a NAME="E31:67"/>
( <span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p2">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp; <span class="p1">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p2">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp; 0 <a href="hidden.html#R1">=</a> 0 <a href="real_1.html#K3">+</a> 0 )
 
<b>by </b><i><a class="ref" href="xreal_1.html#T65">XREAL_1:65</a></i>;<br/>
<a NAME="E32:67"/><b>then </b><i><font color="Green">E127</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p3">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p3">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i><a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/>
<i><font color="Green">E128</font></i>: <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p0"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>,0</span><a href="arytm_0.html#K5">*]</a></span></span>)</span></span><a href="complex1.html#K17">.|</a></span> = 
 <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p5">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p0">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p0"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p5">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p0">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p0"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="complex2.html#T34" target="_self">Th34</a>, <a class="ref" href="complex2.html#T35" target="_self">Th35</a>, <a class="ref" href="complex1.html#D16">COMPLEX1:def 16</a></i>
<br/>.= 
 <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p5"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p5">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p0">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p5">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p0">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p5"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p5">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p0">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p5">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p0">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="complex2.html#T41" target="_self">Th41</a>, , <a class="ref" href="square_1.html#T97">SQUARE_1:97</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p5">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p0">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p5">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p0">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="complex2.html#T26" target="_self">Th26</a>, <a class="ref" href="square_1.html#T89">SQUARE_1:89</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span><a href="complex1.html#K17">.|</a></span>
<b>by </b><i><a class="ref" href="complex1.html#D16">COMPLEX1:def 16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span>
<b>by </b><i/>
;<br/>
<a NAME="E34:67"/><b>then </b><i><font color="Green">E129</font></i>: 
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p0"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>,0</span><a href="arytm_0.html#K5">*]</a></span></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="ref" href="complex2.html#T24" target="_self">Th24</a>, <a class="ref" href="complex2.html#T26" target="_self">Th26</a>, <a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/>
<a NAME="E35:67"/>
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p0"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>,0</span><a href="arytm_0.html#K5">*]</a></span></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K24">cos</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p5">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p0">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>,0</span><a href="arytm_0.html#K5">*]</a></span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p2">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="complex2.html#E21:67"><i><font color="Green">E70</font></i></a>, <a class="ref" href="complex2.html#T34" target="_self">Th34</a>, <a class="ref" href="complex1.html#T28">COMPLEX1:28</a></i>;<br/>
<b>hence </b> <a href="sin_cos.html#K24">cos</a> <span class="p1">(<span class="default"><a href="complex2.html#K3" target="_self">angle</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p3">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p4"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p0"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>,0</span><a href="arytm_0.html#K5">*]</a></span></span>)</span></span><a href="complex1.html#K17">.|</a></span>
<b>by </b><i><a class="txt" href="complex2.html#E19:67"><i><font color="Green">E68</font></i></a>, <a class="ref" href="complex2.html#T43" target="_self">Th43</a>, <a class="ref" href="xcmplx_1.html#T90">XCMPLX_1:90</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p2">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p4"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p5">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p0">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>,0</span><a href="arytm_0.html#K5">*]</a></span></span>)</span></span><a href="complex1.html#K17">.|</a></span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T75">XCMPLX_1:75</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="complex2.html#K1" target="_self">.|.</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p5"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p5"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span>
<b>by </b><i><a class="ref" href="complex2.html#T39" target="_self">Th39</a>, <a class="ref" href="complex2.html#T42" target="_self">Th42</a>, <a class="ref" href="xcmplx_1.html#T79">XCMPLX_1:79</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="complex2.html#K1" target="_self">.|.</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span>
<b>by </b><i><a class="ref" href="complex2.html#T26" target="_self">Th26</a>, <a class="ref" href="xcmplx_1.html#T60">XCMPLX_1:60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="complex2.html#K1" target="_self">.|.</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> 1</span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T77">XCMPLX_1:77</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="complex2.html#K1" target="_self">.|.</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span>

;<br/><br/>

<a NAME="E37:67"/>
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p0"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>,0</span><a href="arytm_0.html#K5">*]</a></span></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K21">sin</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p5">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p0">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>,0</span><a href="arytm_0.html#K5">*]</a></span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p2">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="complex2.html#E21:67"><i><font color="Green">E70</font></i></a>, <a class="ref" href="complex2.html#T35" target="_self">Th35</a>, <a class="ref" href="complex1.html#T28">COMPLEX1:28</a></i>;<br/>
<b>hence </b> <a href="sin_cos.html#K21">sin</a> <span class="p1">(<span class="default"><a href="complex2.html#K3" target="_self">angle</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p3">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p4"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p0"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>,0</span><a href="arytm_0.html#K5">*]</a></span></span>)</span></span><a href="complex1.html#K17">.|</a></span>
<b>by </b><i><a class="txt" href="complex2.html#E19:67"><i><font color="Green">E68</font></i></a>, <a class="ref" href="complex2.html#T43" target="_self">Th43</a>, <a class="ref" href="xcmplx_1.html#T90">XCMPLX_1:90</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p2">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p4"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex2.html#K2" target="_self">Rotate</a> <font color="Maroon">b</font>,<span class="p5">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p0">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>,0</span><a href="arytm_0.html#K5">*]</a></span></span>)</span></span><a href="complex1.html#K17">.|</a></span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T75">XCMPLX_1:75</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p4">(<span class="default"><font color="Maroon">a</font> <a href="complex2.html#K1" target="_self">.|.</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p5"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p5"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span>
<b>by </b><i><a class="ref" href="complex2.html#T40" target="_self">Th40</a>, <a class="ref" href="complex2.html#T42" target="_self">Th42</a>, <a class="ref" href="xcmplx_1.html#T79">XCMPLX_1:79</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p4">(<span class="default"><font color="Maroon">a</font> <a href="complex2.html#K1" target="_self">.|.</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span>
<b>by </b><i><a class="ref" href="complex2.html#T26" target="_self">Th26</a>, <a class="ref" href="xcmplx_1.html#T60">XCMPLX_1:60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p4">(<span class="default"><font color="Maroon">a</font> <a href="complex2.html#K1" target="_self">.|.</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T188">XCMPLX_1:188</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p4">(<span class="default"><font color="Maroon">a</font> <a href="complex2.html#K1" target="_self">.|.</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> 1</span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T77">XCMPLX_1:77</a></i>
<br/>.= 
 <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="complex2.html#K1" target="_self">.|.</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">a</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">b</font></span><a href="complex1.html#K17">.|</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T188">XCMPLX_1:188</a></i>
;<br/><br/>


</div>
