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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><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/>



 <a href="sin_cos.html#K18">exp</a> <span class="p1">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="complex1.html#K9">*</a> <span class="p4"><a href="arytm_0.html#K5">[*</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,0</span><a href="arytm_0.html#K5">*]</a></span></span>)</span> <a href="complex1.html#K9">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> = 
 <a href="sin_cos.html#K18">exp</a> <span class="p1">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p2">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><span class="p4"><a href="arytm_0.html#K5">[*</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,0</span><a href="arytm_0.html#K5">*]</a></span> <a href="complex1.html#K9">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="sin_cos3.html#K2" target="_self">cos_C</a>  <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><span class="p3"><a href="arytm_0.html#K5">[*</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,0</span><a href="arytm_0.html#K5">*]</a></span> <a href="complex1.html#K9">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="complex1.html#K11">-</a> <span class="p1">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="complex1.html#K9">*</a> <span class="p2">(<span class="default"><a href="sin_cos3.html#K1" target="_self">sin_C</a>  <a href="finseq_4.html#K4">/.</a> <span class="p3">(<span class="default"><span class="p4"><a href="arytm_0.html#K5">[*</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,0</span><a href="arytm_0.html#K5">*]</a></span> <a href="complex1.html#K9">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sin_cos3.html#T37" target="_self">Th37</a></i>
;<br/>
<b>hence </b><a NAME="E2:67"/>
 <a href="sin_cos.html#K18">exp</a> <span class="p1">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="complex1.html#K9">*</a> <span class="p4"><a href="arytm_0.html#K5">[*</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,0</span><a href="arytm_0.html#K5">*]</a></span></span>)</span> <a href="complex1.html#K9">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos3.html#K2" target="_self">cos_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="complex1.html#K11">-</a> <span class="p2">(<span class="default"><a href="complex1.html#K7">&lt;i&gt;</a>  <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><a href="sin_cos3.html#K1" target="_self">sin_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="comseq_3.html#K2">#N</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="sin_cos3.html#T52" target="_self">Th52</a></i>;<br/>


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