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

<b>let </b><font color="Maroon">x</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K2">COMPLEX</a> , <font color="Maroon">xv</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">u</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K1">REAL</a> , <font color="Maroon">v</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K1">REAL</a> , <font color="Maroon">uv</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K1">REAL</a> , <font color="Maroon">vv</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K1">REAL</a> ;<br/>



<b>assume </b><a NAME="E1:68"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">u</font> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7">&lt;i&gt;</a> </span>)</span> &amp; <font color="Maroon">xv</font> <a href="hidden.html#R1">=</a> <font color="Maroon">uv</font> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">vv</font> <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7">&lt;i&gt;</a> </span>)</span> )
 ;<br/>

<i><font color="Green">E30</font></i>: <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="complex1.html#K8">+</a> <span class="p3">(<span class="default"><font color="Maroon">xv</font> <a href="complex1.html#K15">*'</a> </span>)</span></span>)</span></span><a href="complex1.html#K17">.|</a></span> = 
 <a href="square_1.html#K6">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">x</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p5">(<span class="default"><font color="Maroon">xv</font> <a href="complex1.html#K15">*'</a> </span>)</span></span>)</span></span>)</span> <a href="square_1.html#K3">^2</a> </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#K4">Im</a> <span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="complex1.html#K8">+</a> <span class="p5">(<span class="default"><font color="Maroon">xv</font> <a href="complex1.html#K15">*'</a> </span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#T19">COMPLEX1:19</a></i>
<br/>.= 
 <a href="square_1.html#K6">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">u</font> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p5">(<span class="default"><font color="Maroon">xv</font> <a href="complex1.html#K15">*'</a> </span>)</span></span>)</span></span>)</span> <a href="square_1.html#K3">^2</a> </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#K4">Im</a> <span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="complex1.html#K8">+</a> <span class="p5">(<span class="default"><font color="Maroon">xv</font> <a href="complex1.html#K15">*'</a> </span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="complex1.html#T28">COMPLEX1:28</a></i>
<br/>.= 
 <a href="square_1.html#K6">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">u</font> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">xv</font></span>)</span></span>)</span> <a href="square_1.html#K3">^2</a> </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#K4">Im</a> <span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="complex1.html#K8">+</a> <span class="p5">(<span class="default"><font color="Maroon">xv</font> <a href="complex1.html#K15">*'</a> </span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#T112">COMPLEX1:112</a></i>
<br/>.= 
 <a href="square_1.html#K6">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">u</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">uv</font></span>)</span> <a href="square_1.html#K3">^2</a> </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#K4">Im</a> <span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="complex1.html#K8">+</a> <span class="p5">(<span class="default"><font color="Maroon">xv</font> <a href="complex1.html#K15">*'</a> </span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="complex1.html#T28">COMPLEX1:28</a></i>
<br/>.= 
 <a href="square_1.html#K6">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">u</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">uv</font></span>)</span> <a href="square_1.html#K3">^2</a> </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#K4">Im</a> <font color="Maroon">x</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p5">(<span class="default"><font color="Maroon">xv</font> <a href="complex1.html#K15">*'</a> </span>)</span></span>)</span></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#T19">COMPLEX1:19</a></i>
<br/>.= 
 <a href="square_1.html#K6">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">u</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">uv</font></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">v</font> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p5">(<span class="default"><font color="Maroon">xv</font> <a href="complex1.html#K15">*'</a> </span>)</span></span>)</span></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="complex1.html#T28">COMPLEX1:28</a></i>
<br/>.= 
 <a href="square_1.html#K6">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">u</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">uv</font></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">v</font> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p5">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">xv</font></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#T112">COMPLEX1:112</a></i>
<br/>.= 
 <a href="square_1.html#K6">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">u</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">uv</font></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">v</font> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">vv</font></span>)</span></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="complex1.html#T28">COMPLEX1:28</a></i>
;<br/>
<a NAME="E3:68"/>
( <span class="p1">(<span class="default"><font color="Maroon">u</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">uv</font></span>)</span> <a href="square_1.html#K3">^2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp; <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">vv</font></span>)</span></span>)</span> <a href="square_1.html#K3">^2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 )
 
<b>by </b><i><a class="ref" href="square_1.html#T72">SQUARE_1:72</a></i>;<br/>
<a NAME="E4:68"/><b>then </b><i><font color="Green">E31</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">u</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">uv</font></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">v</font> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">vv</font></span>)</span></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 <a href="nat_1.html#K1">+</a> 0
 
<b>by </b><i><a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/>
<a NAME="E5:68"/><i><font color="Green">E34</font></i>: 
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="complex1.html#K8">+</a> <span class="p3">(<span class="default"><font color="Maroon">xv</font> <a href="complex1.html#K15">*'</a> </span>)</span></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="square_1.html#K5">^2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">u</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">uv</font></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">v</font> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">vv</font></span>)</span></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>
 
<b>by </b><i>, , <a class="ref" href="square_1.html#D4">SQUARE_1:def 4</a></i>;<br/>
<i><font color="Green">E36</font></i>: <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="complex1.html#K11">-</a> <font color="Maroon">xv</font></span>)</span></span><a href="complex1.html#K17">.|</a></span> = 
 <a href="square_1.html#K6">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">x</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">xv</font></span>)</span></span>)</span> <a href="square_1.html#K3">^2</a> </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#K4">Im</a> <span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="complex1.html#K11">-</a> <font color="Maroon">xv</font></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#T48">COMPLEX1:48</a></i>
<br/>.= 
 <a href="square_1.html#K6">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">u</font> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">xv</font></span>)</span></span>)</span> <a href="square_1.html#K3">^2</a> </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#K4">Im</a> <span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="complex1.html#K11">-</a> <font color="Maroon">xv</font></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="complex1.html#T28">COMPLEX1:28</a></i>
<br/>.= 
 <a href="square_1.html#K6">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">u</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">uv</font></span>)</span> <a href="square_1.html#K3">^2</a> </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#K4">Im</a> <span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="complex1.html#K11">-</a> <font color="Maroon">xv</font></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="complex1.html#T28">COMPLEX1:28</a></i>
<br/>.= 
 <a href="square_1.html#K6">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">u</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">uv</font></span>)</span> <a href="square_1.html#K3">^2</a> </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#K4">Im</a> <font color="Maroon">x</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">xv</font></span>)</span></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#T48">COMPLEX1:48</a></i>
<br/>.= 
 <a href="square_1.html#K6">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">u</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">uv</font></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">v</font> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">xv</font></span>)</span></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="complex1.html#T28">COMPLEX1:28</a></i>
<br/>.= 
 <a href="square_1.html#K6">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">u</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">uv</font></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">v</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">vv</font></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="complex1.html#T28">COMPLEX1:28</a></i>
;<br/>
<a NAME="E7:68"/>
( <span class="p1">(<span class="default"><font color="Maroon">u</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">uv</font></span>)</span> <a href="square_1.html#K3">^2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp; <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">vv</font></span>)</span> <a href="square_1.html#K3">^2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 )
 
<b>by </b><i><a class="ref" href="square_1.html#T72">SQUARE_1:72</a></i>;<br/>
<a NAME="E8:68"/><b>then </b><i><font color="Green">E37</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">u</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">uv</font></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">v</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">vv</font></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 <a href="nat_1.html#K1">+</a> 0
 
<b>by </b><i><a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">u</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">uv</font></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">v</font> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">vv</font></span>)</span></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">u</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">uv</font></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">v</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">vv</font></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">u</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">uv</font></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> 0</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">u</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">uv</font></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">u</font> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">u</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">uv</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">uv</font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">u</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">uv</font></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>
<b>by </b><i><a class="ref" href="square_1.html#T63">SQUARE_1:63</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">u</font> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">u</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">uv</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">uv</font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">u</font> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">u</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">uv</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">uv</font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="square_1.html#T64">SQUARE_1:64</a></i>
<br/>.= 
<span class="p1">(<span class="default">4 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">u</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">uv</font>

;<br/>
<b>hence </b><a NAME="E10:68"/>
<span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="complex1.html#K8">+</a> <span class="p4">(<span class="default"><font color="Maroon">xv</font> <a href="complex1.html#K15">*'</a> </span>)</span></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="complex1.html#K11">-</a> <font color="Maroon">xv</font></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">4 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">u</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">uv</font>
 <b>by </b><i>, , <a class="ref" href="hurwitz.html#T7" target="_self">Th7</a>, <a class="ref" href="square_1.html#D4">SQUARE_1:def 4</a></i>;<br/>


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