<?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">x</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K2">COMPLEX</a> , <font color="Maroon">y</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K2">COMPLEX</a> ;<br/>



<b>assume </b><a NAME="E1:89"/><i><font color="Green">E32</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">y</font>
 ;<br/>

<a NAME="E2:89"/><i><font color="Green">E33</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">x</font>
 
<b>by </b><i><a class="ref" href="complsp2.html#T2" target="_self">Th2</a></i>;<br/>
<a NAME="E3:89"/><i><font color="Green">E36</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">y</font>
 
<b>by </b><i><a class="ref" href="complsp2.html#T2" target="_self">Th2</a></i>;<br/>
<a NAME="E4:89"/><i><font color="Green">E37</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">x</font>
 
<b>by </b><i><a class="ref" href="complsp2.html#T2" target="_self">Th2</a></i>;<br/>
<a NAME="E5:89"/><i><font color="Green">E41</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">y</font>
 
<b>by </b><i><a class="ref" href="complsp2.html#T2" target="_self">Th2</a></i>;<br/>
<a NAME="E6:89"/><i><font color="Green">E42</font></i>: 
 <a href="finseq_1.html#K3">len</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="rvsum_1.html#K9">*</a> <span class="p2">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span>
 
<b>by </b><i><a class="ref" href="euclid_2.html#T8">EUCLID_2:8</a></i>;<br/>
<a NAME="E7:89"/><i><font color="Green">E113</font></i>: 
 <a href="finseq_1.html#K3">len</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="rvsum_1.html#K9">*</a> <span class="p2">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span>
 
<b>by </b><i><a class="ref" href="euclid_2.html#T8">EUCLID_2:8</a></i>;<br/>
<a NAME="E8:89"/><i><font color="Green">E119</font></i>: 
 <a href="finseq_1.html#K3">len</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="rvsum_1.html#K9">*</a> <span class="p2">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span>
 
<b>by </b><i><a class="ref" href="euclid_2.html#T8">EUCLID_2:8</a></i>;<br/>
<a NAME="E9:89"/><i><font color="Green">E120</font></i>: 
 <a href="finseq_1.html#K3">len</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="rvsum_1.html#K9">*</a> <span class="p2">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span>
 
<b>by </b><i><a class="ref" href="euclid_2.html#T8">EUCLID_2:8</a></i>;<br/>
<span class="p1"><a href="complsp2.html#K8" target="_self">|(</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="complsp1.html#K6">*</a> <font color="Maroon">x</font></span>)</span>,<font color="Maroon">y</font></span><a href="complsp2.html#K8" target="_self">)|</a></span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="rvsum_1.html#K7">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p4"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <span class="p0">(<span class="default"><font color="Maroon">a</font> <a href="complsp1.html#K6">*</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p3"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p4">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <span class="p5">(<span class="default"><font color="Maroon">a</font> <a href="complsp1.html#K6">*</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p2">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="complsp1.html#K6">*</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span>
<b>by </b><i><a class="ref" href="complsp2.html#T9" target="_self">Th9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="rvsum_1.html#K7">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p4"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="rvsum_1.html#K7">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p3"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p4">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <span class="p5">(<span class="default"><font color="Maroon">a</font> <a href="complsp1.html#K6">*</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p2">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="complsp1.html#K6">*</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span>
<b>by </b><i><a class="ref" href="complsp2.html#T9" target="_self">Th9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="rvsum_1.html#K7">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p4"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="rvsum_1.html#K7">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p3"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="rvsum_1.html#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p2">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="complsp1.html#K6">*</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span>
<b>by </b><i><a class="ref" href="complsp2.html#T9" target="_self">Th9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="rvsum_1.html#K7">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p4"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="rvsum_1.html#K7">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p3"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="rvsum_1.html#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1"><a href="euclid_2.html#K1">|(</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#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p4">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="rvsum_1.html#K3">+</a> <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="rvsum_1.html#K9">*</a> <span class="p4">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span>
<b>by </b><i><a class="ref" href="complsp2.html#T9" target="_self">Th9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span> <a href="xcmplx_0.html#K6">-</a> <span class="p4"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p4"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="rvsum_1.html#K7">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p3"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="rvsum_1.html#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1"><a href="euclid_2.html#K1">|(</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#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p4">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="rvsum_1.html#K3">+</a> <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="rvsum_1.html#K9">*</a> <span class="p4">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span>
<b>by </b><i><a class="ref" href="euclid_2.html#T25">EUCLID_2:25</a>, <a class="ref" href="complsp2.html#T19" target="_self">Th19</a>, , <a class="ref" href="complsp2.html#T18" target="_self">Th18</a>, , <a class="ref" href="complsp2.html#T20" target="_self">Th20</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span> <a href="xcmplx_0.html#K6">-</a> <span class="p4"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span> <a href="xcmplx_0.html#K6">-</a> <span class="p5"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p3"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="rvsum_1.html#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1"><a href="euclid_2.html#K1">|(</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#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p4">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="rvsum_1.html#K3">+</a> <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="rvsum_1.html#K9">*</a> <span class="p4">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span>
<b>by </b><i><a class="ref" href="euclid_2.html#T25">EUCLID_2:25</a>, <a class="ref" href="complsp2.html#T19" target="_self">Th19</a>, , <a class="ref" href="complsp2.html#T18" target="_self">Th18</a>, , <a class="ref" href="complsp2.html#T20" target="_self">Th20</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span> <a href="xcmplx_0.html#K6">-</a> <span class="p4"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span> <a href="xcmplx_0.html#K6">-</a> <span class="p5"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span> <a href="xcmplx_0.html#K2">+</a> <span class="p4"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1"><a href="euclid_2.html#K1">|(</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#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p4">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="rvsum_1.html#K3">+</a> <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="rvsum_1.html#K9">*</a> <span class="p4">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span>
<b>by </b><i><a class="ref" href="euclid_2.html#T19">EUCLID_2:19</a>, <a class="ref" href="complsp2.html#T19" target="_self">Th19</a>, , <a class="ref" href="complsp2.html#T18" target="_self">Th18</a>, <a class="ref" href="complsp2.html#T21" target="_self">Th21</a>, , <a class="ref" href="complsp2.html#T24" target="_self">Th24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span> <a href="xcmplx_0.html#K6">-</a> <span class="p4"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span> <a href="xcmplx_0.html#K6">-</a> <span class="p5"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span> <a href="xcmplx_0.html#K2">+</a> <span class="p4"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2"><a href="euclid_2.html#K1">|(</a><span class="default"><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="rvsum_1.html#K9">*</a> <span class="p4">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span> <a href="xcmplx_0.html#K2">+</a> <span class="p2"><a href="euclid_2.html#K1">|(</a><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="rvsum_1.html#K9">*</a> <span class="p4">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span>
<b>by </b><i><a class="ref" href="euclid_2.html#T19">EUCLID_2:19</a>, <a class="ref" href="complsp2.html#T19" target="_self">Th19</a>, , <a class="ref" href="complsp2.html#T18" target="_self">Th18</a>, <a class="ref" href="complsp2.html#T21" target="_self">Th21</a>, , <a class="ref" href="complsp2.html#T24" target="_self">Th24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span> <a href="xcmplx_0.html#K6">-</a> <span class="p4"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p0"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p1">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span>,<span class="p1">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p5"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span> <a href="xcmplx_0.html#K2">+</a> <span class="p4"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2"><a href="euclid_2.html#K1">|(</a><span class="default"><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="rvsum_1.html#K9">*</a> <span class="p4">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span> <a href="xcmplx_0.html#K2">+</a> <span class="p2"><a href="euclid_2.html#K1">|(</a><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="rvsum_1.html#K9">*</a> <span class="p4">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span>
<b>by </b><i><a class="ref" href="euclid_2.html#T20">EUCLID_2:20</a>, <a class="ref" href="complsp2.html#T19" target="_self">Th19</a>, <a class="ref" href="complsp2.html#T18" target="_self">Th18</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span> <a href="xcmplx_0.html#K6">-</a> <span class="p4"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p0"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p1">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span>,<span class="p1">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p0"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p1">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span>,<span class="p1">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span> <a href="xcmplx_0.html#K2">+</a> <span class="p4"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2"><a href="euclid_2.html#K1">|(</a><span class="default"><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="rvsum_1.html#K9">*</a> <span class="p4">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span> <a href="xcmplx_0.html#K2">+</a> <span class="p2"><a href="euclid_2.html#K1">|(</a><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="rvsum_1.html#K9">*</a> <span class="p4">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span>
<b>by </b><i><a class="ref" href="euclid_2.html#T20">EUCLID_2:20</a>, , <a class="ref" href="complsp2.html#T18" target="_self">Th18</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"><span class="p5">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p5"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p0"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p1">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span>,<span class="p1">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p0"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p1">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span>,<span class="p1">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span> <a href="xcmplx_0.html#K2">+</a> <span class="p4"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2"><a href="euclid_2.html#K1">|(</a><span class="default"><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="rvsum_1.html#K9">*</a> <span class="p4">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span> <a href="xcmplx_0.html#K2">+</a> <span class="p2"><a href="euclid_2.html#K1">|(</a><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="rvsum_1.html#K9">*</a> <span class="p4">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span>
<b>by </b><i><a class="ref" href="euclid_2.html#T20">EUCLID_2:20</a>, <a class="ref" href="complsp2.html#T19" target="_self">Th19</a>, <a class="ref" href="complsp2.html#T18" target="_self">Th18</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"><span class="p5">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p5"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p5"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p0"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p1">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span>,<span class="p1">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p0"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p1">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span>,<span class="p1">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span> <a href="xcmplx_0.html#K2">+</a> <span class="p4"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2"><a href="euclid_2.html#K1">|(</a><span class="default"><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="rvsum_1.html#K9">*</a> <span class="p4">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span> <a href="xcmplx_0.html#K2">+</a> <span class="p2"><a href="euclid_2.html#K1">|(</a><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="rvsum_1.html#K9">*</a> <span class="p4">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span>
<b>by </b><i><a class="ref" href="euclid_2.html#T20">EUCLID_2:20</a>, , <a class="ref" href="complsp2.html#T18" target="_self">Th18</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"><span class="p5">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p5"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p5"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p0"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p1">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span>,<span class="p1">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p0"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p1">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span>,<span class="p1">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p5"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="rvsum_1.html#K9">*</a> <span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2"><a href="euclid_2.html#K1">|(</a><span class="default"><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="rvsum_1.html#K9">*</a> <span class="p4">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span> <a href="xcmplx_0.html#K2">+</a> <span class="p2"><a href="euclid_2.html#K1">|(</a><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="rvsum_1.html#K9">*</a> <span class="p4">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span>
<b>by </b><i><a class="ref" href="euclid_2.html#T20">EUCLID_2:20</a>, <a class="ref" href="complsp2.html#T19" target="_self">Th19</a>, <a class="ref" href="complsp2.html#T18" target="_self">Th18</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"><span class="p5">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p5"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p5"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p0"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p1">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span>,<span class="p1">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p0"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p1">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span>,<span class="p1">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p5"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span> <a href="xcmplx_0.html#K2">+</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="xcmplx_0.html#K3">*</a> <span class="p5"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</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"><a href="euclid_2.html#K1">|(</a><span class="default"><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="rvsum_1.html#K9">*</a> <span class="p4">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span> <a href="xcmplx_0.html#K2">+</a> <span class="p2"><a href="euclid_2.html#K1">|(</a><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="rvsum_1.html#K9">*</a> <span class="p4">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span>
<b>by </b><i><a class="ref" href="euclid_2.html#T20">EUCLID_2:20</a>, , <a class="ref" href="complsp2.html#T18" target="_self">Th18</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"><span class="p5">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p5"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p5"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p0"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p1">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span>,<span class="p1">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p0"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p1">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span>,<span class="p1">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p5"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span> <a href="xcmplx_0.html#K2">+</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="xcmplx_0.html#K3">*</a> <span class="p5"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</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">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p3"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p4">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span>,<span class="p4">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2"><a href="euclid_2.html#K1">|(</a><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="rvsum_1.html#K9">*</a> <span class="p4">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span>
<b>by </b><i><a class="ref" href="euclid_2.html#T20">EUCLID_2:20</a>, <a class="ref" href="complsp2.html#T19" target="_self">Th19</a>, <a class="ref" href="complsp2.html#T18" target="_self">Th18</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"><span class="p5">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p5"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p5"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p0"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p1">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span>,<span class="p1">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p0"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p1">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span>,<span class="p1">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p5"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span> <a href="xcmplx_0.html#K2">+</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="xcmplx_0.html#K3">*</a> <span class="p5"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</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">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p3"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p4">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span>,<span class="p4">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span> <a href="xcmplx_0.html#K2">+</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="xcmplx_0.html#K3">*</a> <span class="p3"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p4">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span>,<span class="p4">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclid_2.html#T20">EUCLID_2:20</a>, , <a class="ref" href="complsp2.html#T18" target="_self">Th18</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"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p0"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p1">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span>,<span class="p1">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p0"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p1">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span>,<span class="p1">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7">&lt;i&gt;</a> </span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p5"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</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="xcmplx_0.html#K3">*</a> <span class="p4"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</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> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p5"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</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="xcmplx_0.html#K3">*</a> <span class="p4"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></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">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p3">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span>,<span class="p3">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></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"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p0"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p1">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span>,<span class="p1">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p0"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p1">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span>,<span class="p1">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7">&lt;i&gt;</a> </span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p5"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</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="xcmplx_0.html#K3">*</a> <span class="p4"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</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> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p5">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p4"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <span class="p2"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p3">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span>,<span class="p3">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#T29">COMPLEX1:29</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"><span class="p5">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p5"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p0">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p5"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><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="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p0">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p5"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p4"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <span class="p2"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p3">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span>,<span class="p3">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#T29">COMPLEX1:29</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"><span class="p5">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p0">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p4"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p5"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p4"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <span class="p2"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p3">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span>,<span class="p3">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#T29">COMPLEX1:29</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <span class="p4"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p5"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">x</font></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3">*</a> <span class="p4"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" target="_self">Re</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <span class="p2"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p3">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">x</font></span>)</span>,<span class="p3">(<span class="default"><a href="complsp2.html#K7" target="_self">Im</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span></span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#T29">COMPLEX1:29</a></i>
<br/>.= 
<font color="Maroon">a</font> <a href="binop_2.html#K5">*</a> <span class="p1"><a href="complsp2.html#K8" target="_self">|(</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="complsp2.html#K8" target="_self">)|</a></span>

;<br/>
<b>hence </b><a NAME="E11:89"/>
<span class="p1"><a href="complsp2.html#K8" target="_self">|(</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="complsp1.html#K6">*</a> <font color="Maroon">x</font></span>)</span>,<font color="Maroon">y</font></span><a href="complsp2.html#K8" target="_self">)|</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="binop_2.html#K5">*</a> <span class="p1"><a href="complsp2.html#K8" target="_self">|(</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="complsp2.html#K8" target="_self">)|</a></span>
 ;<br/>


</div>
