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<b>let </b><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</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="E1:76"/><i><font color="Green" title="E65">A1</font></i>: 
( <font color="Maroon" title="c1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">y</font> &amp; <font color="Maroon" title="c3">z</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">y</font> )
 ;<br/>

<a NAME="E2:76"/><b>then </b><i><font color="Green" title="E66">A2</font></i>: 
<font color="Maroon" title="c1">x</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c2">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> 
 
;<br/>
<a NAME="E3:76"/><i><font color="Green" title="E67">A3</font></i>: 
<font color="Maroon" title="c3">z</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c2">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> 
 
<b>by </b><i><a class="txt" href="complex2.html#E1:76"><i><font color="Green" title="E65">A1</font></i></a></i>;<br/>
<a NAME="E4:76"/>
 <a href="complex2.html#K4" title="COMPLEX2:func.4">angle</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex2.html#K4" title="COMPLEX2:func.4">angle</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c2">y</font></span>)</span>,<a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> ,<span class="p1">(<span class="default"><font color="Maroon" title="c3">z</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c2">y</font></span>)</span>
 
<b>by </b><i><a class="ref" href="complex2.html#T85" target="_self" title="COMPLEX2:th.85">Th85</a></i>;<br/>
<b>hence </b><a NAME="E5:76"/>
(  <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="complex2.html#K1" title="COMPLEX2:func.1">.|.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">z</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 iff (  <a href="complex2.html#K4" title="COMPLEX2:func.4">angle</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a>  <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2 or  <a href="complex2.html#K4" title="COMPLEX2:func.4">angle</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">3 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2</span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a>  ) )
 <b>by </b><i><a class="txt" href="complex2.html#E2:76"><i><font color="Green" title="E66">A2</font></i></a>, <a class="txt" href="complex2.html#E3:76"><i><font color="Green" title="E67">A3</font></i></a>, <a class="ref" href="complex2.html#T89" target="_self" title="COMPLEX2:th.89">Th89</a></i>;<br/>


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