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

<b>let </b><font color="Maroon">z1</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">z2</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">z3</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">z</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K2">COMPLEX</a> ;<br/>







<b>assume </b><a NAME="E1:33"/><i><font color="Green">E46</font></i>: 
( <font color="Maroon">z1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 &amp;  <a href="polyeq_1.html#K3">Polynom</a> <font color="Maroon">z1</font>,<font color="Maroon">z2</font>,<font color="Maroon">z3</font>,<font color="Maroon">z</font> <a href="hidden.html#R1">=</a> 0 )
 ;<br/>

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



<b>assume </b><a NAME="E2:33"/><i><font color="Green">E47</font></i>: 
( <font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z2</font> <a href="complex1.html#K13">/</a> <span class="p3">(<span class="default">2 <a href="polyeq_3.html#K1" target="_self">*</a> <font color="Maroon">z1</font></span>)</span></span>)</span> <a href="polyeq_3.html#K3" target="_self">^2</a> </span>)</span> <a href="complex1.html#K11">-</a> <span class="p1">(<span class="default"><font color="Maroon">z3</font> <a href="complex1.html#K13">/</a> <font color="Maroon">z1</font></span>)</span> &amp; <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z2</font> <a href="complex1.html#K13">/</a> <span class="p1">(<span class="default">2 <a href="polyeq_3.html#K1" target="_self">*</a> <font color="Maroon">z1</font></span>)</span> )
 ;<br/>

<a NAME="E3:33"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">z1</font> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="polyeq_3.html#K3" target="_self">^2</a> </span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p3">(<span class="default"><font color="Maroon">z2</font> <a href="complex1.html#K9">*</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <font color="Maroon">z3</font></span>)</span> <a href="complex1.html#K13">/</a> <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i/>;<br/>
<a NAME="E4:33"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="polyeq_3.html#K3" target="_self">^2</a> </span>)</span> <a href="complex1.html#K9">*</a> <font color="Maroon">z1</font></span>)</span> <a href="complex1.html#K13">/</a> <font color="Maroon">z1</font></span>)</span> <a href="complex1.html#K8">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">z2</font> <a href="complex1.html#K9">*</a> <font color="Maroon">z</font></span>)</span> <a href="complex1.html#K13">/</a> <font color="Maroon">z1</font></span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p1">(<span class="default"><font color="Maroon">z3</font> <a href="complex1.html#K13">/</a> <font color="Maroon">z1</font></span>)</span> <a href="hidden.html#R1">=</a> 0
 
;<br/>
<a NAME="E5:33"/><b>then </b><i><font color="Green">E48</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="polyeq_3.html#K3" target="_self">^2</a> </span>)</span> <a href="complex1.html#K8">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">z2</font> <a href="complex1.html#K13">/</a> <font color="Maroon">z1</font></span>)</span> <a href="complex1.html#K9">*</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p1">(<span class="default"><font color="Maroon">z3</font> <a href="complex1.html#K13">/</a> <font color="Maroon">z1</font></span>)</span> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i>, <a class="ref" href="xcmplx_1.html#T90">XCMPLX_1:90</a></i>;<br/>
<a NAME="E6:33"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="polyeq_3.html#K3" target="_self">^2</a> </span>)</span> <a href="complex1.html#K8">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="polyeq_3.html#K1" target="_self">*</a> <font color="Maroon">z2</font></span>)</span> <a href="complex1.html#K13">/</a> <span class="p4">(<span class="default">2 <a href="polyeq_3.html#K1" target="_self">*</a> <font color="Maroon">z1</font></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p1">(<span class="default"><font color="Maroon">z3</font> <a href="complex1.html#K13">/</a> <font color="Maroon">z1</font></span>)</span> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i>, <a class="ref" href="xcmplx_1.html#T92">XCMPLX_1:92</a></i>;<br/>
<a NAME="E7:33"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="complex1.html#K8">+</a> <span class="p3">(<span class="default"><font color="Maroon">z2</font> <a href="complex1.html#K13">/</a> <span class="p4">(<span class="default">2 <a href="polyeq_3.html#K1" target="_self">*</a> <font color="Maroon">z1</font></span>)</span></span>)</span></span>)</span> <a href="polyeq_3.html#K3" target="_self">^2</a> </span>)</span> <a href="complex1.html#K11">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">z2</font> <a href="complex1.html#K13">/</a> <span class="p4">(<span class="default">2 <a href="polyeq_3.html#K1" target="_self">*</a> <font color="Maroon">z1</font></span>)</span></span>)</span> <a href="polyeq_3.html#K3" target="_self">^2</a> </span>)</span> <a href="complex1.html#K11">-</a> <span class="p2">(<span class="default"><font color="Maroon">z3</font> <a href="complex1.html#K13">/</a> <font color="Maroon">z1</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0
 
;<br/>
<a NAME="E8:33"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="complex1.html#K8">+</a> <font color="Maroon">t</font></span>)</span> <a href="complex1.html#K11">-</a> <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K7">sqrt</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">h</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">h</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">h</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span> <a href="polyeq_3.html#K2" target="_self">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">h</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p0">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">h</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">h</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span> <a href="polyeq_3.html#K1" target="_self">*</a> <a href="complex1.html#K7">&lt;i&gt;</a> </span>)</span></span>)</span> <a href="complex1.html#K11">-</a> <font color="Maroon">t</font> or <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="complex1.html#K8">+</a> <font color="Maroon">t</font></span>)</span> <a href="complex1.html#K11">-</a> <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K7">sqrt</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">h</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p0">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">h</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">h</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span>)</span> <a href="polyeq_3.html#K2" target="_self">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">h</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">h</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">h</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span>)</span> <a href="polyeq_3.html#K1" target="_self">*</a> <a href="complex1.html#K7">&lt;i&gt;</a> </span>)</span></span>)</span> <a href="complex1.html#K11">-</a> <font color="Maroon">t</font> or <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="complex1.html#K8">+</a> <font color="Maroon">t</font></span>)</span> <a href="complex1.html#K11">-</a> <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K7">sqrt</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">h</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">h</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">h</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span> <a href="polyeq_3.html#K2" target="_self">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">h</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">h</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">h</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span>)</span> <a href="polyeq_3.html#K1" target="_self">*</a> <a href="complex1.html#K7">&lt;i&gt;</a> </span>)</span></span>)</span> <a href="complex1.html#K11">-</a> <font color="Maroon">t</font> or <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="complex1.html#K8">+</a> <font color="Maroon">t</font></span>)</span> <a href="complex1.html#K11">-</a> <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K7">sqrt</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">h</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p0">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">h</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">h</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span>)</span> <a href="polyeq_3.html#K2" target="_self">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">h</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p0">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">h</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">h</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span> <a href="polyeq_3.html#K1" target="_self">*</a> <a href="complex1.html#K7">&lt;i&gt;</a> </span>)</span></span>)</span> <a href="complex1.html#K11">-</a> <font color="Maroon">t</font> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E9:33"/>
( <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K7">sqrt</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">h</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">h</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">h</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span> <a href="polyeq_3.html#K2" target="_self">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">h</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p0">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">h</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span 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href="polyeq_3.html#K1" target="_self">*</a> <a href="complex1.html#K7">&lt;i&gt;</a> </span>)</span></span>)</span> <a href="complex1.html#K11">-</a> <font color="Maroon">t</font> )
 ;<br/>


</div>
