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<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="E1:32"/>
 <a href="euclid_3.html#K3" target="_self">Arg</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> 0
 ;<br/>

<a NAME="E2:32"/><b>then </b>
 <a href="comptrig.html#K1">Arg</a> <span class="p1">(<span class="default"><a href="euclid_3.html#K2" target="_self">euc2cpx</a> <font color="Maroon">p</font></span>)</span> <a href="hidden.html#R1">=</a> 0
 
;<br/>
<a NAME="E3:32"/><b>then </b><i><font color="Green">E41</font></i>: 
(  <a href="euclid_3.html#K2" target="_self">euc2cpx</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><span class="p3">(<span class="default"><a href="euclid_3.html#K2" target="_self">euc2cpx</a> <font color="Maroon">p</font></span>)</span></span><a href="complex1.html#K17">.|</a></span>,0</span><a href="arytm_0.html#K5">*]</a></span> &amp;  <a href="complex1.html#K4">Im</a> <span class="p1">(<span class="default"><a href="euclid_3.html#K2" target="_self">euc2cpx</a> <font color="Maroon">p</font></span>)</span> <a href="hidden.html#R1">=</a> 0 )
 
<b>by </b><i><a class="ref" href="complex2.html#T24">COMPLEX2:24</a>, <a class="ref" href="complex2.html#T34">COMPLEX2:34</a></i>;<br/>
<a NAME="E4:32"/><i><font color="Green">E49</font></i>: 
 <a href="euclid_3.html#K1" target="_self">cpx2euc</a> <span class="p1"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><span class="p3">(<span class="default"><a href="euclid_3.html#K2" target="_self">euc2cpx</a> <font color="Maroon">p</font></span>)</span></span><a href="complex1.html#K17">.|</a></span>,0</span><a href="arytm_0.html#K5">*]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><span class="p3">(<span class="default"><a href="euclid_3.html#K2" target="_self">euc2cpx</a> <font color="Maroon">p</font></span>)</span></span><a href="complex1.html#K17">.|</a></span>,0</span><a href="euclid.html#K23">]|</a></span>
 
<b>by </b><i/>;<br/>
<a NAME="E5:32"/>
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><a href="euclid_3.html#K2" target="_self">euc2cpx</a> <font color="Maroon">p</font></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">p</font></span><a href="toprns_1.html#K5">.|</a></span>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E6:32"/>
( <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">p</font></span><a href="toprns_1.html#K5">.|</a></span>,0</span><a href="euclid.html#K23">]|</a></span> &amp; <font color="Maroon">p</font> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> 0 )
 <b>by </b><i>, , , </i>;<br/>


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