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<b>let </b><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c2">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies  <a href="complex2.html#K3" title="COMPLEX2:func.3">angle</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex2.html#K3" title="COMPLEX2:func.3">angle</a> <span class="p1">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <font color="Maroon" title="c1">a</font></span>)</span>,<span class="p1">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <font color="Maroon" title="c2">b</font></span>)</span> )</span><br/>



<b>assume </b><a NAME="E1:64"/>
( <font color="Maroon" title="c1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c2">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="complex2.html#K3" title="COMPLEX2:func.3">angle</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex2.html#K3" title="COMPLEX2:func.3">angle</a> <span class="p1">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <font color="Maroon" title="c1">a</font></span>)</span>,<span class="p1">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <font color="Maroon" title="c2">b</font></span>)</span></span><br/>

<b>hence </b> <a href="complex2.html#K3" title="COMPLEX2:func.3">angle</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> = 
 <a href="complex2.html#K3" title="COMPLEX2:func.3">angle</a> <span class="p1">(<span class="default"><a href="complex2.html#K2" title="COMPLEX2:func.2">Rotate</a> <font color="Maroon" title="c1">a</font>,<a href="sin_cos.html#K36" title="SIN_COS:func.36">PI</a> </span>)</span>,<span class="p1">(<span class="default"><a href="complex2.html#K2" title="COMPLEX2:func.2">Rotate</a> <font color="Maroon" title="c2">b</font>,<a href="sin_cos.html#K36" title="SIN_COS:func.36">PI</a> </span>)</span>
<b>by </b><i><a class="ref" href="complex2.html#T79" target="_self" title="COMPLEX2:th.79">Th79</a></i>
<br/>.= 
 <a href="complex2.html#K3" title="COMPLEX2:func.3">angle</a> <span class="p1">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <font color="Maroon" title="c1">a</font></span>)</span>,<span class="p1">(<span class="default"><a href="complex2.html#K2" title="COMPLEX2:func.2">Rotate</a> <font color="Maroon" title="c2">b</font>,<a href="sin_cos.html#K36" title="SIN_COS:func.36">PI</a> </span>)</span>
<b>by </b><i><a class="ref" href="complex2.html#T74" target="_self" title="COMPLEX2:th.74">Th74</a></i>
<br/>.= 
 <a href="complex2.html#K3" title="COMPLEX2:func.3">angle</a> <span class="p1">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <font color="Maroon" title="c1">a</font></span>)</span>,<span class="p1">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <font color="Maroon" title="c2">b</font></span>)</span>
<b>by </b><i><a class="ref" href="complex2.html#T74" target="_self" title="COMPLEX2:th.74">Th74</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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