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

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

<b>set </b><font color="Maroon">e1</font> =  <a href="sin_cos.html#K18">exp</a> <font color="Maroon">z</font>;<br/>
<b>set </b><font color="Maroon">e2</font> =  <a href="sin_cos.html#K18">exp</a> <span class="p1">(<span class="default"><a href="complex1.html#K10">-</a> <font color="Maroon">z</font></span>)</span>;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">z</font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p2">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="complex1.html#K11">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">z</font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p2">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">z</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">z</font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p2">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K18">exp</a> <font color="Maroon">z</font></span>)</span> <a href="complex1.html#K11">-</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K18">exp</a> <span class="p5">(<span class="default"><a href="complex1.html#K10">-</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">z</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">z</font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p2">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K18">exp</a> <font color="Maroon">z</font></span>)</span> <a href="complex1.html#K11">-</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K18">exp</a> <span class="p5">(<span class="default"><a href="complex1.html#K10">-</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K18">exp</a> <font color="Maroon">z</font></span>)</span> <a href="complex1.html#K11">-</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K18">exp</a> <span class="p5">(<span class="default"><a href="complex1.html#K10">-</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K18">exp</a> <font color="Maroon">z</font></span>)</span> <a href="complex1.html#K8">+</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K18">exp</a> <span class="p5">(<span class="default"><a href="complex1.html#K10">-</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K18">exp</a> <font color="Maroon">z</font></span>)</span> <a href="complex1.html#K11">-</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K18">exp</a> <span class="p5">(<span class="default"><a href="complex1.html#K10">-</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K18">exp</a> <font color="Maroon">z</font></span>)</span> <a href="complex1.html#K11">-</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K18">exp</a> <span class="p5">(<span class="default"><a href="complex1.html#K10">-</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K2">*</a> 2</span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K18">exp</a> <font color="Maroon">z</font></span>)</span> <a href="complex1.html#K8">+</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K18">exp</a> <span class="p5">(<span class="default"><a href="complex1.html#K10">-</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K18">exp</a> <font color="Maroon">z</font></span>)</span> <a href="complex1.html#K8">+</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K18">exp</a> <span class="p5">(<span class="default"><a href="complex1.html#K10">-</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K18">exp</a> <font color="Maroon">z</font></span>)</span> <a href="complex1.html#K11">-</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K18">exp</a> <span class="p5">(<span class="default"><a href="complex1.html#K10">-</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K18">exp</a> <font color="Maroon">z</font></span>)</span> <a href="complex1.html#K11">-</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K18">exp</a> <span class="p5">(<span class="default"><a href="complex1.html#K10">-</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K2">*</a> 2</span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K18">exp</a> <font color="Maroon">z</font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K18">exp</a> <span class="p5">(<span class="default"><a href="complex1.html#K10">-</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K18">exp</a> <font color="Maroon">z</font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K18">exp</a> <span class="p5">(<span class="default"><a href="complex1.html#K10">-</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K18">exp</a> <font color="Maroon">z</font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K18">exp</a> <span class="p5">(<span class="default"><a href="complex1.html#K10">-</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K18">exp</a> <font color="Maroon">z</font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K18">exp</a> <span class="p5">(<span class="default"><a href="complex1.html#K10">-</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 2</span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K18">exp</a> <font color="Maroon">z</font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K18">exp</a> <span class="p5">(<span class="default"><a href="complex1.html#K10">-</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K18">exp</a> <font color="Maroon">z</font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K18">exp</a> <span class="p5">(<span class="default"><a href="complex1.html#K10">-</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K18">exp</a> <font color="Maroon">z</font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K18">exp</a> <span class="p5">(<span class="default"><a href="complex1.html#K10">-</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 2</span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K18">exp</a> <font color="Maroon">z</font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K18">exp</a> <span class="p5">(<span class="default"><a href="complex1.html#K10">-</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K18">exp</a> <font color="Maroon">z</font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K18">exp</a> <span class="p5">(<span class="default"><a href="complex1.html#K10">-</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 2</span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K18">exp</a> <font color="Maroon">z</font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K18">exp</a> <span class="p5">(<span class="default"><a href="complex1.html#K10">-</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 2</span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 2</span>)</span>
<b>by </b><i/>
<br/>.= 
1

;<br/>
<b>hence </b><a NAME="E2:17"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">z</font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p2">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="complex1.html#K11">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">z</font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p2">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 1
 ;<br/>


</div>
