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

<b>let </b><font color="Maroon">z</font> be  <a href="xcmplx_0.html#V1">complex</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<b>assume </b><a NAME="E1:1"/>
<font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> <a href="complex1.html#K15">*'</a> 
 ;<br/>

<a NAME="E2:1"/><b>then </b>
 <a href="complex1.html#K4">Im</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> 0 <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">z</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="complex1.html#T112">COMPLEX1:112</a></i>;<br/>
<a NAME="E3:1"/><b>then </b>
<span class="p1">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">z</font></span>)</span> <a href="real_1.html#K5">-</a> 0 <a href="hidden.html#R1">=</a> 0 <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">z</font></span>)</span>
 
;<br/>
<a NAME="E4:1"/><b>then </b>
<span class="p1">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">z</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">z</font></span>)</span> <a href="hidden.html#R1">=</a> 0 <a href="real_1.html#K3">+</a> 0
 
;<br/>
<a NAME="E5:1"/><b>then </b>
2 <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">z</font></span>)</span> <a href="hidden.html#R1">=</a> 0
 
;<br/>
<b>hence </b><a NAME="E6:1"/>
 <a href="complex1.html#K4">Im</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> 0
 ;<br/>


</div>
