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

<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>let </b><font color="Maroon">p</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/>



<b>assume </b><a NAME="E1:29"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="euclid_3.html#K2" target="_self">euc2cpx</a> <font color="Maroon">p</font> or <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="euclid_3.html#K1" target="_self">cpx2euc</a> <font color="Maroon">z</font> )
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:29_1"/>
( <font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="euclid_3.html#K2" target="_self">euc2cpx</a> <font color="Maroon">p</font> or <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="euclid_3.html#K1" target="_self">cpx2euc</a> <font color="Maroon">z</font> )
 </span><b>by </b><i/>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_1"><b>suppose </b></a><a NAME="E1:29_1_1"/>
<font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="euclid_3.html#K2" target="_self">euc2cpx</a> <font color="Maroon">p</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:29_1_1"/>
 <a href="comptrig.html#K1">Arg</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="euclid_3.html#K3" target="_self">Arg</a> <font color="Maroon">p</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_2"><b>suppose </b></a><a NAME="E1:29_1_2"/>
<font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="euclid_3.html#K1" target="_self">cpx2euc</a> <font color="Maroon">z</font>
 ;<br/><div class="add"><a NAME="E2:29_1_2"/><b>then </b>
 <a href="euclid_3.html#K2" target="_self">euc2cpx</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:29_1_2"/>
 <a href="comptrig.html#K1">Arg</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="euclid_3.html#K3" target="_self">Arg</a> <font color="Maroon">p</font>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
