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

<b>let </b><font color="Maroon" title="c1">z1</font>, <font color="Maroon" title="c2">z2</font>, <font color="Maroon" title="c3">z</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> ;<br/>





<b>assume </b><a NAME="E1:36"/><i><font color="Green" title="E13">A1</font></i>: 
( <font color="Maroon" title="c1">z1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp;  <a href="polyeq_1.html#K7" title="POLYEQ_1:func.7">Polynom</a> <font color="Maroon" title="c1">z1</font>,<font color="Maroon" title="c2">z2</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<font color="Maroon" title="c3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 ;<br/>

<a NAME="E2:36"/><b>then </b>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">z1</font> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <font color="Maroon" title="c3">z</font></span>)</span> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <font color="Maroon" title="c2">z2</font></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">z</font> <a href="polyeq_3.html#K3" title="POLYEQ_3:func.3">^2</a> </span>)</span>
 
;<br/>
<a NAME="E3:36"/><b>then </b>
(  <a href="polyeq_1.html#K1" title="POLYEQ_1:func.1">Polynom</a> <font color="Maroon" title="c1">z1</font>,<font color="Maroon" title="c2">z2</font>,<font color="Maroon" title="c3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="polyeq_3.html#K1" title="POLYEQ_3:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">z</font> <a href="polyeq_3.html#K3" title="POLYEQ_3:func.3">^2</a> </span>)</span></span>)</span> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <span class="p2">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="polyeq_3.html#K1" title="POLYEQ_3:func.1">*</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T6" title="XCMPLX_1:th.6">XCMPLX_1:6</a></i>;<br/>
<a NAME="E4:36"/><b>then </b>
( <font color="Maroon" title="c3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">z2</font> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <font color="Maroon" title="c1">z1</font></span>)</span> or  <a href="polyeq_1.html#K3" title="POLYEQ_1:func.3">Polynom</a> <a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> ,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<font color="Maroon" title="c3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 
<b>by </b><i><a class="txt" href="polyeq_3.html#E1:36"><i><font color="Green" title="E13">A1</font></i></a>, <a class="ref" href="polyeq_3.html#T24" target="_self" title="POLYEQ_3:th.24">Th24</a></i>;<br/>
<b>hence </b><a NAME="E5:36"/>
( <font color="Maroon" title="c3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">z2</font> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <font color="Maroon" title="c1">z1</font></span>)</span> or <font color="Maroon" title="c3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 <b>by </b><i><a class="ref" href="polyeq_3.html#T34" target="_self" title="POLYEQ_3:th.34">Th34</a>, <a class="ref" href="complex1.html#D7" title="COMPLEX1:def.7">COMPLEX1:def 7</a></i>;<br/>


</div>
