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<b>let </b><font color="Maroon">a</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">b</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">c</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K2">COMPLEX</a> ;<br/>





<b>assume </b><a NAME="E1:91"/><i><font color="Green">E23</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font> &amp;  <a href="complex2.html#K4" target="_self">angle</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="hidden.html#R1">=</a> 0 )
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="91_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:91_1"/>
( (  <a href="complex2.html#K4" target="_self">angle</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 0 &amp;  <a href="complex2.html#K4" target="_self">angle</a> <font color="Maroon">c</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="hidden.html#R1">=</a>  <a href="sin_cos.html#K35">PI</a>  ) or (  <a href="complex2.html#K4" target="_self">angle</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="sin_cos.html#K35">PI</a>  &amp;  <a href="complex2.html#K4" target="_self">angle</a> <font color="Maroon">c</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="hidden.html#R1">=</a> 0 ) )
 </span><b>by </b><i><a class="ref" href="complex2.html#T40" target="_self">Th40</a>, <a class="ref" href="complex2.html#T38" target="_self">Th38</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="91_1_1"><b>suppose </b></a><a NAME="E1:91_1_1"/>
(  <a href="complex2.html#K4" target="_self">angle</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 0 &amp;  <a href="complex2.html#K4" target="_self">angle</a> <font color="Maroon">c</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="hidden.html#R1">=</a>  <a href="sin_cos.html#K35">PI</a>  )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:91_1_1"/>
<span class="p1">(<span class="default"><a href="complex2.html#K4" target="_self">angle</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="complex2.html#K4" target="_self">angle</a> <font color="Maroon">c</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="sin_cos.html#K35">PI</a> 
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="91_1_2"><b>suppose </b></a><a NAME="E1:91_1_2"/>
(  <a href="complex2.html#K4" target="_self">angle</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="sin_cos.html#K35">PI</a>  &amp;  <a href="complex2.html#K4" target="_self">angle</a> <font color="Maroon">c</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="hidden.html#R1">=</a> 0 )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:91_1_2"/>
<span class="p1">(<span class="default"><a href="complex2.html#K4" target="_self">angle</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="complex2.html#K4" target="_self">angle</a> <font color="Maroon">c</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="sin_cos.html#K35">PI</a> 
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

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