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<b>let </b><font color="Maroon" title="c1">z</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> ;<br/>

<a NAME="E1:27"/>
<a href="sin_cos3.html#K4" title="SIN_COS3:func.4">cosh_C</a>  <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K18" title="SIN_COS:func.18">exp</a> <span class="p3">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <font color="Maroon" title="c1">z</font></span>)</span></span>)</span> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <span class="p2">(<span class="default"><a href="sin_cos.html#K18" title="SIN_COS:func.18">exp</a> <span class="p3">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <span class="p4">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <font color="Maroon" title="c1">z</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2
 
<b>by </b><i><a class="txt" href="sin_cos3.html#E9"><i><font color="Green" title="E9">Lm5</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:27"/>
<a href="sin_cos3.html#K4" title="SIN_COS3:func.4">cosh_C</a>  <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="sin_cos3.html#K2" title="SIN_COS3:func.2">cos_C</a>  <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c1">z</font>
 <b>by </b><i><a class="txt" href="sin_cos3.html#E7"><i><font color="Green" title="E7">Lm3</font></i></a></i>;<br/>


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