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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K2">COMPLEX</a> ;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:68"/><i><font color="Green">E65</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>and </b><br/><a NAME="E2:68"/><i><font color="Green">E66</font></i>: 
 <a href="complex2.html#K4" target="_self">angle</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/>

<a NAME="E3:68"/><i><font color="Green">E67</font></i>: 
 <a href="complex1.html#K10">-</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="txt" href="complex2.html#E1:68"><i><font color="Green">E65</font></i></a></i>;<br/>
<a NAME="E4:68"/><i><font color="Green">E68</font></i>: 
 <a href="comptrig.html#K1">Arg</a> <span class="p1">(<span class="default"><a href="complex2.html#K3" target="_self">Rotate</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="complex2.html#E1:68"><i><font color="Green">E65</font></i></a>, <a class="txt" href="complex2.html#E2:68"><i><font color="Green">E66</font></i></a>, <a class="ref" href="complex2.html#D5" target="_self">Def5</a></i>;<br/>
<a NAME="E5:68"/><i><font color="Green">E69</font></i>: 
 <a href="complex2.html#K3" target="_self">Rotate</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="txt" href="complex2.html#E1:68"><i><font color="Green">E65</font></i></a>, <a class="ref" href="complex2.html#T66" target="_self">Th66</a></i>;<br/>
<a NAME="E6:68"/><i><font color="Green">E70</font></i>: 
 <a href="comptrig.html#K1">Arg</a> <span class="p1">(<span class="default"><a href="complex2.html#K3" target="_self">Rotate</a> <span class="p2">(<span class="default"><a href="complex1.html#K10">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="comptrig.html#K1">Arg</a> <span class="p1">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p2">(<span class="default"><a href="complex2.html#K3" target="_self">Rotate</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="complex2.html#T72" target="_self">Th72</a></i>;<br/>
 <a href="comptrig.html#K1">Arg</a> <span class="p1">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p2">(<span class="default"><a href="complex2.html#K3" target="_self">Rotate</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="comptrig.html#K1">Arg</a> <span class="p2">(<span class="default"><a href="complex2.html#K3" target="_self">Rotate</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <a href="sin_cos.html#K33">PI</a> 
<b>by </b><i><a class="txt" href="complex2.html#E4:68"><i><font color="Green">E68</font></i></a>, <a class="txt" href="complex2.html#E5:68"><i><font color="Green">E69</font></i></a>, <a class="ref" href="complex2.html#T22" target="_self">Th22</a>, <a class="ref" href="comptrig.html#T21">COMPTRIG:21</a></i>
<br/>.= 
 <a href="sin_cos.html#K33">PI</a> 
<b>by </b><i><a class="txt" href="complex2.html#E4:68"><i><font color="Green">E68</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E8:68"/>
 <a href="complex2.html#K4" target="_self">angle</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="complex1.html#K10">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="sin_cos.html#K33">PI</a> 
 <b>by </b><i><a class="txt" href="complex2.html#E3:68"><i><font color="Green">E67</font></i></a>, <a class="txt" href="complex2.html#E6:68"><i><font color="Green">E70</font></i></a>, <a class="ref" href="complex2.html#D5" target="_self">Def5</a></i>;<br/>


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