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

<b>let </b><font color="Maroon" title="c1">x1</font>, <font color="Maroon" title="c2">x2</font>, <font color="Maroon" title="c3">y</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> ;<br/>

<b>assume </b><a NAME="E1:77"/><i><font color="Green" title="E67">A1</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">x2</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">y</font> )
 ;<br/>

<a NAME="E2:77"/><i><font color="Green" title="E68">A2</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c1">x1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">x1</font>
 
<b>by </b><i><a class="ref" href="complsp2.html#T48" target="_self" title="COMPLSP2:th.48">Th48</a></i>;<br/>
<a NAME="E3:77"/><i><font color="Green" title="E69">A3</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c2">x2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">x2</font>
 
<b>by </b><i><a class="ref" href="complsp2.html#T48" target="_self" title="COMPLSP2:th.48">Th48</a></i>;<br/>
<a NAME="E4:77"/><i><font color="Green" title="E70">A4</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">y</font>
 
<b>by </b><i><a class="ref" href="complsp2.html#T48" target="_self" title="COMPLSP2:th.48">Th48</a></i>;<br/>
<a NAME="E5:77"/><i><font color="Green" title="E71">A5</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c1">x1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">x1</font>
 
<b>by </b><i><a class="ref" href="complsp2.html#T48" target="_self" title="COMPLSP2:th.48">Th48</a></i>;<br/>
<a NAME="E6:77"/><i><font color="Green" title="E72">A6</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c2">x2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">x2</font>
 
<b>by </b><i><a class="ref" href="complsp2.html#T48" target="_self" title="COMPLSP2:th.48">Th48</a></i>;<br/>
<a NAME="E7:77"/><i><font color="Green" title="E73">A7</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">y</font>
 
<b>by </b><i><a class="ref" href="complsp2.html#T48" target="_self" title="COMPLSP2:th.48">Th48</a></i>;<br/>
<span class="p1"><a href="complsp2.html#K8" title="COMPLSP2:func.8">|(</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x1</font> <a href="complsp1.html#K3" title="COMPLSP1:func.3">+</a> <font color="Maroon" title="c2">x2</font></span>)</span>,<font color="Maroon" title="c3">y</font></span><a href="complsp2.html#K8" title="COMPLSP2:func.8">)|</a></span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c1">x1</font></span>)</span> <a href="rvsum_1.html#K4" title="RVSUM_1:func.4">+</a> <span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c2">x2</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p4"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <span class="p0">(<span class="default"><font color="Maroon" title="c1">x1</font> <a href="complsp1.html#K3" title="COMPLSP1:func.3">+</a> <font color="Maroon" title="c2">x2</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p4">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">x1</font> <a href="complsp1.html#K3" title="COMPLSP1:func.3">+</a> <font color="Maroon" title="c2">x2</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p2">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">x1</font> <a href="complsp1.html#K3" title="COMPLSP1:func.3">+</a> <font color="Maroon" title="c2">x2</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span>
<b>by </b><i><a class="txt" href="complsp2.html#E1:77"><i><font color="Green" title="E67">A1</font></i></a>, <a class="ref" href="complsp2.html#T49" target="_self" title="COMPLSP2:th.49">Th49</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c1">x1</font></span>)</span> <a href="rvsum_1.html#K4" title="RVSUM_1:func.4">+</a> <span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c2">x2</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p4"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c1">x1</font></span>)</span> <a href="rvsum_1.html#K4" title="RVSUM_1:func.4">+</a> <span class="p0">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c2">x2</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p4">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">x1</font> <a href="complsp1.html#K3" title="COMPLSP1:func.3">+</a> <font color="Maroon" title="c2">x2</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p2">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">x1</font> <a href="complsp1.html#K3" title="COMPLSP1:func.3">+</a> <font color="Maroon" title="c2">x2</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span>
<b>by </b><i><a class="txt" href="complsp2.html#E1:77"><i><font color="Green" title="E67">A1</font></i></a>, <a class="ref" href="complsp2.html#T49" target="_self" title="COMPLSP2:th.49">Th49</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c1">x1</font></span>)</span> <a href="rvsum_1.html#K4" title="RVSUM_1:func.4">+</a> <span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c2">x2</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p4"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c1">x1</font></span>)</span> <a href="rvsum_1.html#K4" title="RVSUM_1:func.4">+</a> <span class="p0">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c2">x2</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c1">x1</font></span>)</span> <a href="rvsum_1.html#K4" title="RVSUM_1:func.4">+</a> <span class="p5">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c2">x2</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p2">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">x1</font> <a href="complsp1.html#K3" title="COMPLSP1:func.3">+</a> <font color="Maroon" title="c2">x2</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span>
<b>by </b><i><a class="txt" href="complsp2.html#E1:77"><i><font color="Green" title="E67">A1</font></i></a>, <a class="ref" href="complsp2.html#T49" target="_self" title="COMPLSP2:th.49">Th49</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c1">x1</font></span>)</span> <a href="rvsum_1.html#K4" title="RVSUM_1:func.4">+</a> <span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c2">x2</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p4"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c1">x1</font></span>)</span> <a href="rvsum_1.html#K4" title="RVSUM_1:func.4">+</a> <span class="p0">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c2">x2</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c1">x1</font></span>)</span> <a href="rvsum_1.html#K4" title="RVSUM_1:func.4">+</a> <span class="p5">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c2">x2</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c1">x1</font></span>)</span> <a href="rvsum_1.html#K4" title="RVSUM_1:func.4">+</a> <span class="p3">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c2">x2</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span>
<b>by </b><i><a class="txt" href="complsp2.html#E1:77"><i><font color="Green" title="E67">A1</font></i></a>, <a class="ref" href="complsp2.html#T49" target="_self" title="COMPLSP2:th.49">Th49</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#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c1">x1</font></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p4"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c2">x2</font></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p4"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c1">x1</font></span>)</span> <a href="rvsum_1.html#K4" title="RVSUM_1:func.4">+</a> <span class="p0">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c2">x2</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c1">x1</font></span>)</span> <a href="rvsum_1.html#K4" title="RVSUM_1:func.4">+</a> <span class="p5">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c2">x2</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c1">x1</font></span>)</span> <a href="rvsum_1.html#K4" title="RVSUM_1:func.4">+</a> <span class="p3">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c2">x2</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span>
<b>by </b><i><a class="txt" href="complsp2.html#E1:77"><i><font color="Green" title="E67">A1</font></i></a>, <a class="txt" href="complsp2.html#E2:77"><i><font color="Green" title="E68">A2</font></i></a>, <a class="txt" href="complsp2.html#E3:77"><i><font color="Green" title="E69">A3</font></i></a>, <a class="txt" href="complsp2.html#E4:77"><i><font color="Green" title="E70">A4</font></i></a>, <a class="ref" href="euclid_2.html#T19" title="EUCLID_2:th.19">EUCLID_2:19</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#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c1">x1</font></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p4"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c2">x2</font></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p4">(<span class="default"><span class="p5"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c1">x1</font></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p5"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c2">x2</font></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c1">x1</font></span>)</span> <a href="rvsum_1.html#K4" title="RVSUM_1:func.4">+</a> <span class="p5">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c2">x2</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c1">x1</font></span>)</span> <a href="rvsum_1.html#K4" title="RVSUM_1:func.4">+</a> <span class="p3">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c2">x2</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span>
<b>by </b><i><a class="txt" href="complsp2.html#E1:77"><i><font color="Green" title="E67">A1</font></i></a>, <a class="txt" href="complsp2.html#E2:77"><i><font color="Green" title="E68">A2</font></i></a>, <a class="txt" href="complsp2.html#E3:77"><i><font color="Green" title="E69">A3</font></i></a>, <a class="txt" href="complsp2.html#E7:77"><i><font color="Green" title="E73">A7</font></i></a>, <a class="ref" href="euclid_2.html#T19" title="EUCLID_2:th.19">EUCLID_2:19</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#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c1">x1</font></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p4"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c2">x2</font></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p4">(<span class="default"><span class="p5"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c1">x1</font></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p5"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c2">x2</font></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><span class="p4"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c1">x1</font></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p4"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c2">x2</font></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c1">x1</font></span>)</span> <a href="rvsum_1.html#K4" title="RVSUM_1:func.4">+</a> <span class="p3">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c2">x2</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span>
<b>by </b><i><a class="txt" href="complsp2.html#E1:77"><i><font color="Green" title="E67">A1</font></i></a>, <a class="txt" href="complsp2.html#E4:77"><i><font color="Green" title="E70">A4</font></i></a>, <a class="txt" href="complsp2.html#E5:77"><i><font color="Green" title="E71">A5</font></i></a>, <a class="txt" href="complsp2.html#E6:77"><i><font color="Green" title="E72">A6</font></i></a>, <a class="ref" href="euclid_2.html#T19" title="EUCLID_2:th.19">EUCLID_2:19</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#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c1">x1</font></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p4"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c2">x2</font></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p4">(<span class="default"><span class="p5"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c1">x1</font></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p5"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p0">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c2">x2</font></span>)</span>,<span class="p0">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><span class="p4"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c1">x1</font></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p4"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p5">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c2">x2</font></span>)</span>,<span class="p5">(<span class="default"><a href="complsp2.html#K6" title="COMPLSP2:func.6">Re</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p3">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c1">x1</font></span>)</span>,<span class="p3">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p2"><a href="euclid_2.html#K2" title="EUCLID_2:func.2">|(</a><span class="default"><span class="p3">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c2">x2</font></span>)</span>,<span class="p3">(<span class="default"><a href="complsp2.html#K7" title="COMPLSP2:func.7">Im</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="euclid_2.html#K2" title="EUCLID_2:func.2">)|</a></span></span>)</span>
<b>by </b><i><a class="txt" href="complsp2.html#E1:77"><i><font color="Green" title="E67">A1</font></i></a>, <a class="txt" href="complsp2.html#E5:77"><i><font color="Green" title="E71">A5</font></i></a>, <a class="txt" href="complsp2.html#E6:77"><i><font color="Green" title="E72">A6</font></i></a>, <a class="txt" href="complsp2.html#E7:77"><i><font color="Green" title="E73">A7</font></i></a>, <a class="ref" href="euclid_2.html#T19" title="EUCLID_2:th.19">EUCLID_2:19</a></i>
<br/>.= 
<span class="p1"><a href="complsp2.html#K8" title="COMPLSP2:func.8">|(</a><span class="default"><font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c3">y</font></span><a href="complsp2.html#K8" title="COMPLSP2:func.8">)|</a></span> <a href="binop_2.html#K3" title="BINOP_2:func.3">+</a> <span class="p1"><a href="complsp2.html#K8" title="COMPLSP2:func.8">|(</a><span class="default"><font color="Maroon" title="c2">x2</font>,<font color="Maroon" title="c3">y</font></span><a href="complsp2.html#K8" title="COMPLSP2:func.8">)|</a></span>

;<br/>
<b>hence </b><a NAME="E9:77"/>
<span class="p1"><a href="complsp2.html#K8" title="COMPLSP2:func.8">|(</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x1</font> <a href="complsp1.html#K3" title="COMPLSP1:func.3">+</a> <font color="Maroon" title="c2">x2</font></span>)</span>,<font color="Maroon" title="c3">y</font></span><a href="complsp2.html#K8" title="COMPLSP2:func.8">)|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="complsp2.html#K8" title="COMPLSP2:func.8">|(</a><span class="default"><font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c3">y</font></span><a href="complsp2.html#K8" title="COMPLSP2:func.8">)|</a></span> <a href="binop_2.html#K3" title="BINOP_2:func.3">+</a> <span class="p1"><a href="complsp2.html#K8" title="COMPLSP2:func.8">|(</a><span class="default"><font color="Maroon" title="c2">x2</font>,<font color="Maroon" title="c3">y</font></span><a href="complsp2.html#K8" title="COMPLSP2:func.8">)|</a></span>
 ;<br/>


</div>
