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<b>let </b><font color="Maroon">x</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K2">COMPLEX</a> , <font color="Maroon">y</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K2">COMPLEX</a> , <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="E1:76"/><i><font color="Green">E23</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y</font> &amp; <font color="Maroon">z</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y</font> )
 ;<br/>

<a NAME="E2:76"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">x</font> <a href="complex1.html#K11">-</a> <font color="Maroon">y</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="complex1.html#K5">0c</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E3:76"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">z</font> <a href="complex1.html#K11">-</a> <font color="Maroon">y</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="complex1.html#K5">0c</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E4:76"/>
 <a href="complex2.html#K4" target="_self">angle</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="complex2.html#K4" target="_self">angle</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="complex1.html#K11">-</a> <font color="Maroon">y</font></span>)</span>,<a href="complex1.html#K5">0c</a> ,<span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="complex1.html#K11">-</a> <font color="Maroon">y</font></span>)</span>
 
<b>by </b><i><a class="ref" href="complex2.html#T23" target="_self">Th23</a></i>;<br/>
<b>hence </b><a NAME="E5:76"/>
(  <a href="complex1.html#K3">Re</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="complex1.html#K11">-</a> <font color="Maroon">y</font></span>)</span> <a href="complex2.html#K1" target="_self">.|.</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="complex1.html#K11">-</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0 iff (  <a href="complex2.html#K4" target="_self">angle</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <a href="sin_cos.html#K35">PI</a>  <a href="real_1.html#K6">/</a> 2 or  <a href="complex2.html#K4" target="_self">angle</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">3 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K35">PI</a>  ) )
 <b>by </b><i>, <a class="ref" href="complex2.html#T27" target="_self">Th27</a>, </i>;<br/>


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