<?xml version="1.0"?>
<div class="add">

<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>thus </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sin_cos.html#K6" target="_self">ExpSeq</a> </span>)</span> <a href="comseq_1.html#K1">.</a> 0 = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="newton.html#K2">|^</a> 0</span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">0 <a href="sin_cos.html#K4" target="_self">!c</a> </span>)</span>
<b>by </b><i><a class="ref" href="sin_cos.html#D8" target="_self">Def8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="comseq_3.html#K1">GeoSeq</a> </span>)</span> <a href="comseq_1.html#K1">.</a> 0</span>)</span> <a href="complex1.html#K13">/</a> <span class="p1">(<span class="default">0 <a href="sin_cos.html#K4" target="_self">!c</a> </span>)</span>

<br/>.= 
1
<b>by </b><i><a class="ref" href="sin_cos.html#T1" target="_self">Th1</a>, <a class="ref" href="comseq_3.html#D1">COMSEQ_3:def 1</a>, <a class="ref" href="complex1.html#D7">COMPLEX1:def 7</a></i>
;<br/>

<a NAME="E2:30"/><i><font color="Green">E24</font></i>: 
0 <a href="binarith.html#K5">-'</a> 0 <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="binarith.html#T51">BINARITH:51</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="sin_cos.html#K11" target="_self">Expan</a> 0,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="comseq_1.html#K1">.</a> 0 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos.html#K8" target="_self">Coef</a> 0</span>)</span> <a href="comseq_1.html#K1">.</a> 0</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="newton.html#K2">|^</a> 0</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="newton.html#K2">|^</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="sin_cos.html#D13" target="_self">Def13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default">1 <a href="nat_1.html#K2">*</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="newton.html#K2">|^</a> 0</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="newton.html#K2">|^</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="sin_cos.html#E2:30"><i><font color="Green">E24</font></i></a>, <a class="ref" href="sin_cos.html#D10" target="_self">Def10</a>, <a class="ref" href="sin_cos.html#T1" target="_self">Th1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="comseq_3.html#K1">GeoSeq</a> </span>)</span> <a href="comseq_1.html#K1">.</a> 0</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="newton.html#K2">|^</a> 0</span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="comseq_3.html#K1">GeoSeq</a> </span>)</span> <a href="comseq_1.html#K1">.</a> 0</span>)</span> <a href="complex1.html#K9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="comseq_3.html#K1">GeoSeq</a> </span>)</span> <a href="comseq_1.html#K1">.</a> 0</span>)</span>

<br/>.= 
<a href="complex1.html#K6">1r</a>  <a href="complex1.html#K9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="comseq_3.html#K1">GeoSeq</a> </span>)</span> <a href="comseq_1.html#K1">.</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="comseq_3.html#D1">COMSEQ_3:def 1</a></i>
<br/>.= 
1
<b>by </b><i><a class="ref" href="comseq_3.html#D1">COMSEQ_3:def 1</a>, <a class="ref" href="complex1.html#D7">COMPLEX1:def 7</a></i>
;<br/><br/>


</div>
