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

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></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="E1:90"/><i><font color="Green">E83</font></i>: 
 <a href="complex1.html#K4">Im</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0
 <b>and </b><br/><a NAME="E2:90"/><i><font color="Green">E84</font></i>: 
 <a href="complex1.html#K3">Re</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>and </b><br/><a NAME="E3:90"/><i><font color="Green">E85</font></i>: 
 <a href="comptrig.html#K1">Arg</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="sin_cos.html#K33">PI</a> 
 ;<br/>

<a NAME="E4:90"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">c<sub>1</sub></font></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="txt" href="complex2.html#E1:90"><i><font color="Green">E83</font></i></a>, <a class="ref" href="complex1.html#T29">COMPLEX1:29</a></i>;<br/>
<a NAME="E5:90"/><b>then </b><i><font color="Green">E86</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span>
 
<b>by </b><i><a class="ref" href="hahnban1.html#D1">HAHNBAN1:def 1</a></i>;<br/>
<a NAME="E6:90"/><i><font color="Green">E87</font></i>: 
 <a href="comptrig.html#K1">Arg</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="complex2.html#E2:90"><i><font color="Green">E84</font></i></a>, <a class="txt" href="complex2.html#E5:90"><i><font color="Green">E86</font></i></a>, <a class="ref" href="comptrig.html#T53">COMPTRIG:53</a></i>;<br/>
<b>then </b><i><font color="Green">E88</font></i>:  <a href="comptrig.html#K1">Arg</a> <span class="p1">(<span class="default"><a href="complex1.html#K10">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <a href="sin_cos.html#K33">PI</a> 
<b>by </b><i><a class="txt" href="complex2.html#E2:90"><i><font color="Green">E84</font></i></a>, <a class="ref" href="complex2.html#T22" target="_self">Th22</a>, <a class="ref" href="complex1.html#T12">COMPLEX1:12</a>, <a class="ref" href="comptrig.html#T21">COMPTRIG:21</a></i>
<br/>.= 
 <a href="sin_cos.html#K33">PI</a> 
<b>by </b><i><a class="txt" href="complex2.html#E6:90"><i><font color="Green">E87</font></i></a></i>
;<br/>
<a NAME="E8:90"/><i><font color="Green">E89</font></i>: 
(  <a href="complex1.html#K3">Re</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;</a> 0 &amp;  <a href="complex1.html#K4">Im</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 0 )
 
<b>by </b><i><a class="txt" href="complex2.html#E3:90"><i><font color="Green">E85</font></i></a>, <a class="ref" href="complex2.html#T35" target="_self">Th35</a></i>;<br/>
<i><font color="Green">E90</font></i>:  <a href="complex1.html#K4">Im</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#T48">COMPLEX1:48</a></i>
<br/>.= 
 <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="complex2.html#E1:90"><i><font color="Green">E83</font></i></a></i>
;<br/>
<a NAME="E10:90"/><i><font color="Green">E91</font></i>: 
<span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K3">+</a> 0 <a href="xxreal_0.html#R1">&lt;</a>  <a href="complex1.html#K3">Re</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="complex2.html#E2:90"><i><font color="Green">E84</font></i></a>, <a class="txt" href="complex2.html#E8:90"><i><font color="Green">E89</font></i></a></i>;<br/>
<a NAME="E11:90"/><b>then </b>
<span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="ref" href="xreal_1.html#T22">XREAL_1:22</a></i>;<br/>
<a NAME="E12:90"/><b>then </b><i><font color="Green">E92</font></i>: 
 <a href="complex1.html#K3">Re</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="ref" href="complex1.html#T48">COMPLEX1:48</a></i>;<br/>
<a NAME="E13:90"/><b>then </b><i><font color="Green">E93</font></i>: 
 <a href="comptrig.html#K1">Arg</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="complex2.html#E8:90"><i><font color="Green">E89</font></i></a>, <a class="txt" href="complex2.html#E9:90"><i><font color="Green">E90</font></i></a>, <a class="ref" href="complex2.html#T34" target="_self">Th34</a></i>;<br/>
<a NAME="E14:90"/>
 <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"><a href="complex1.html#K3">Re</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="txt" href="complex2.html#E10:90"><i><font color="Green">E91</font></i></a>, <a class="ref" href="xreal_1.html#T22">XREAL_1:22</a></i>;<br/>
<a NAME="E15:90"/><b>then </b>
<span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> 0
 
<b>by </b><i><a class="ref" href="xreal_1.html#T60">XREAL_1:60</a></i>;<br/>
<a NAME="E16:90"/><b>then </b><i><font color="Green">E94</font></i>: 
 <a href="complex1.html#K3">Re</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> 0
 
<b>by </b><i><a class="ref" href="complex1.html#T48">COMPLEX1:48</a></i>;<br/>
<i><font color="Green">E95</font></i>:  <a href="complex1.html#K4">Im</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#T48">COMPLEX1:48</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="complex2.html#E1:90"><i><font color="Green">E83</font></i></a>, <a class="txt" href="complex2.html#E3:90"><i><font color="Green">E85</font></i></a>, <a class="ref" href="complex2.html#T35" target="_self">Th35</a></i>
;<br/>
<a NAME="E18:90"/><b>then </b><i><font color="Green">E96</font></i>: 
 <a href="comptrig.html#K1">Arg</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="sin_cos.html#K33">PI</a> 
 
<b>by </b><i><a class="txt" href="complex2.html#E16:90"><i><font color="Green">E94</font></i></a>, <a class="ref" href="complex2.html#T35" target="_self">Th35</a></i>;<br/>
<a NAME="E19:90"/>
<span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complex1.html#K11">-</a> <a href="complex1.html#K5">0c</a> </span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complex1.html#K11">-</a> <a href="complex1.html#K5">0c</a> </span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="txt" href="complex2.html#E3:90"><i><font color="Green">E85</font></i></a>, <a class="txt" href="complex2.html#E6:90"><i><font color="Green">E87</font></i></a>, <a class="ref" href="comptrig.html#T21">COMPTRIG:21</a></i>;<br/>
<a NAME="E20:90"/><b>then </b><i><font color="Green">E97</font></i>: 
 <a href="complex2.html#K5" target="_self">angle</a> <font color="Maroon">c<sub>1</sub></font>,<a href="complex1.html#K5">0c</a> ,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="complex2.html#D6" target="_self">Def6</a></i>;<br/>
<a NAME="E21:90"/><i><font color="Green">E98</font></i>: 
 <a href="comptrig.html#K1">Arg</a> <span class="p1">(<span class="default"><a href="complex1.html#K10">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <a href="sin_cos.html#K33">PI</a> 
 
<b>by </b><i><a class="txt" href="complex2.html#E3:90"><i><font color="Green">E85</font></i></a>, <a class="ref" href="complex2.html#T20" target="_self">Th20</a>, <a class="ref" href="complex2.html#T22" target="_self">Th22</a>, <a class="ref" href="comptrig.html#T21">COMPTRIG:21</a></i>;<br/>
<a NAME="E22:90"/>
<span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="complex2.html#E3:90"><i><font color="Green">E85</font></i></a>, <a class="txt" href="complex2.html#E18:90"><i><font color="Green">E96</font></i></a></i>;<br/>
<a NAME="E23:90"/><b>then </b>
<span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p2">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 0
 
;<br/>
<a NAME="E24:90"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <a href="sin_cos.html#K33">PI</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="complex2.html#E12:90"><i><font color="Green">E92</font></i></a>, <a class="txt" href="complex2.html#E13:90"><i><font color="Green">E93</font></i></a>, <a class="ref" href="complex2.html#T22" target="_self">Th22</a>, <a class="ref" href="complex1.html#T12">COMPLEX1:12</a>, <a class="ref" href="comptrig.html#T21">COMPTRIG:21</a></i>;<br/>
<a NAME="E25:90"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <a href="sin_cos.html#K33">PI</a> </span>)</span> <a href="real_1.html#K5">-</a> <a href="sin_cos.html#K33">PI</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p2">(<span class="default"><a href="complex1.html#K10">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="complex2.html#E21:90"><i><font color="Green">E98</font></i></a></i>;<br/>
<a NAME="E26:90"/><b>then </b><i><font color="Green">E99</font></i>: 
<span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p2">(<span class="default"><a href="complex1.html#K5">0c</a>  <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0
 
;<br/>
<a NAME="E27:90"/><b>then </b><i><font color="Green">E100</font></i>: 
 <a href="complex2.html#K5" target="_self">angle</a> <a href="complex1.html#K5">0c</a> ,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p2">(<span class="default"><a href="complex1.html#K5">0c</a>  <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="complex2.html#D6" target="_self">Def6</a></i>;<br/>
<a NAME="E28:90"/><b>then </b><i><font color="Green">E101</font></i>: 
 <a href="complex2.html#K5" target="_self">angle</a> <a href="complex1.html#K5">0c</a> ,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p2">(<span class="default"><a href="complex1.html#K10">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T150">XCMPLX_1:150</a></i>;<br/>
<a NAME="E29:90"/>
 <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> <a href="sin_cos.html#K33">PI</a> 
 
<b>by </b><i><a class="txt" href="complex2.html#E16:90"><i><font color="Green">E94</font></i></a>, <a class="txt" href="complex2.html#E17:90"><i><font color="Green">E95</font></i></a>, <a class="ref" href="complex2.html#T35" target="_self">Th35</a></i>;<br/>
<a NAME="E30:90"/><b>then </b>
<span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p2">(<span class="default"><a href="complex1.html#K10">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <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> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="complex2.html#E7:90"><i><font color="Green">E88</font></i></a></i>;<br/>
<a NAME="E31:90"/><b>then </b>
<span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p2">(<span class="default"><a href="complex1.html#K10">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0
 
;<br/>
<a NAME="E32:90"/><b>then </b>
<span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p2">(<span class="default"><a href="complex1.html#K5">0c</a>  <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0
 
;<br/>
<a NAME="E33:90"/><b>then </b><i><font color="Green">E102</font></i>: 
 <a href="complex2.html#K5" target="_self">angle</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<a href="complex1.html#K5">0c</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p2">(<span class="default"><a href="complex1.html#K5">0c</a>  <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="complex2.html#D6" target="_self">Def6</a></i>;<br/>
<a NAME="E34:90"/><i><font color="Green">E103</font></i>: 
 <a href="comptrig.html#K1">Arg</a> <span class="p1">(<span class="default"><a href="complex1.html#K10">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <a href="sin_cos.html#K33">PI</a> 
 
<b>by </b><i><a class="txt" href="complex2.html#E3:90"><i><font color="Green">E85</font></i></a>, <a class="ref" href="complex2.html#T20" target="_self">Th20</a>, <a class="ref" href="complex2.html#T22" target="_self">Th22</a>, <a class="ref" href="comptrig.html#T21">COMPTRIG:21</a></i>;<br/>
<i><font color="Green">E104</font></i>: <span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p2">(<span class="default"><a href="complex1.html#K10">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <a href="sin_cos.html#K33">PI</a> </span>)</span>
<b>by </b><i><a class="txt" href="complex2.html#E2:90"><i><font color="Green">E84</font></i></a>, <a class="txt" href="complex2.html#E6:90"><i><font color="Green">E87</font></i></a>, <a class="ref" href="complex2.html#T22" target="_self">Th22</a>, <a class="ref" href="complex1.html#T12">COMPLEX1:12</a>, <a class="ref" href="comptrig.html#T21">COMPTRIG:21</a></i>
<br/>.= 
 <a href="real_1.html#K1">-</a> <a href="sin_cos.html#K33">PI</a> 

;<br/>
<b>thus </b><i><font color="Green">E105</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex2.html#K5" target="_self">angle</a> <font color="Maroon">c<sub>1</sub></font>,0,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="complex2.html#K5" target="_self">angle</a> 0,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="complex2.html#K5" target="_self">angle</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font>,0</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">c<sub>1</sub></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="comptrig.html#K1">Arg</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p4">(<span class="default"><a href="complex1.html#K10">-</a> <font color="Maroon">c<sub>2</sub></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="comptrig.html#K1">Arg</a> <span class="p3">(<span class="default">0 <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="complex2.html#E20:90"><i><font color="Green">E97</font></i></a>, <a class="txt" href="complex2.html#E28:90"><i><font color="Green">E101</font></i></a>, <a class="txt" href="complex2.html#E33:90"><i><font color="Green">E102</font></i></a></i>
<br/>.= 
<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="comptrig.html#K1">Arg</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p5">(<span class="default"><a href="complex1.html#K10">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>2</sub></font></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="comptrig.html#K1">Arg</a> <span class="p3">(<span class="default">0 <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>

<br/>.= 
<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="comptrig.html#K1">Arg</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p5">(<span class="default"><a href="complex1.html#K10">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>2</sub></font></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="comptrig.html#K1">Arg</a> <span class="p3">(<span class="default"><a href="complex1.html#K10">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos.html#K33">PI</a>  <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p4">(<span class="default"><a href="complex1.html#K10">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="complex2.html#E34:90"><i><font color="Green">E103</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K33">PI</a>  <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <a href="sin_cos.html#K33">PI</a> </span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="complex2.html#E35:90"><i><font color="Green">E104</font></i></a></i>
<br/>.= 
<a href="sin_cos.html#K33">PI</a>  <a href="real_1.html#K3">+</a> 0
<b>by </b><i><a class="txt" href="complex2.html#E13:90"><i><font color="Green">E93</font></i></a>, <a class="txt" href="complex2.html#E18:90"><i><font color="Green">E96</font></i></a></i>
<br/>.= 
 <a href="sin_cos.html#K33">PI</a> 

;<br/>

<b>thus </b><a NAME="E37:90"/>
0 <a href="hidden.html#R1">=</a>  <a href="complex2.html#K5" target="_self">angle</a> 0,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="complex2.html#E26:90"><i><font color="Green">E99</font></i></a>, <a class="ref" href="complex2.html#D6" target="_self">Def6</a></i>;<br/>

<b>thus </b><a NAME="E38:90"/>
0 <a href="hidden.html#R1">=</a>  <a href="complex2.html#K5" target="_self">angle</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font>,0
 <b>by </b><i><a class="txt" href="complex2.html#E3:90"><i><font color="Green">E85</font></i></a>, <a class="txt" href="complex2.html#E6:90"><i><font color="Green">E87</font></i></a>, <a class="txt" href="complex2.html#E20:90"><i><font color="Green">E97</font></i></a>, <a class="txt" href="complex2.html#E26:90"><i><font color="Green">E99</font></i></a>, <a class="txt" href="complex2.html#E27:90"><i><font color="Green">E100</font></i></a>, <a class="txt" href="complex2.html#E36:90"><i><font color="Green">E105</font></i></a>, <a class="ref" href="xcmplx_1.html#T3">XCMPLX_1:3</a></i>;<br/>


</div>
