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<b>let </b><font color="Maroon" title="c3">z</font>, <font color="Maroon" title="c4">z1</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/>



<span class="p1">(<span class="default"><a href="comseq_3.html#K8" title="COMSEQ_3:func.8">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <font color="Maroon" title="c3">z</font></span>)</span> <a href="sin_cos.html#K6" title="SIN_COS:func.6">ExpSeq</a> </span>)</span></span>)</span> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <span class="p1">(<span class="default"><a href="comseq_3.html#K8" title="COMSEQ_3:func.8">Sum</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="sin_cos.html#K6" title="SIN_COS:func.6">ExpSeq</a> </span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="comseq_3.html#K8" title="COMSEQ_3:func.8">Sum</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="sin_cos.html#K6" title="SIN_COS:func.6">ExpSeq</a> </span>)</span></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p2">(<span class="default"><a href="comseq_3.html#K8" title="COMSEQ_3:func.8">Sum</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">z</font> <a href="sin_cos.html#K6" title="SIN_COS:func.6">ExpSeq</a> </span>)</span></span>)</span></span>)</span> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="comseq_3.html#K8" title="COMSEQ_3:func.8">Sum</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="sin_cos.html#K6" title="SIN_COS:func.6">ExpSeq</a> </span>)</span></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> </span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#D7" title="COMPLEX1:def.7">COMPLEX1:def 7</a>, <a class="txt" href="sin_cos.html#E42"><i><font color="Green" title="E36">Lm2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="comseq_3.html#K8" title="COMSEQ_3:func.8">Sum</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="sin_cos.html#K6" title="SIN_COS:func.6">ExpSeq</a> </span>)</span></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</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="comseq_3.html#K8" title="COMSEQ_3:func.8">Sum</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">z</font> <a href="sin_cos.html#K6" title="SIN_COS:func.6">ExpSeq</a> </span>)</span></span>)</span> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> </span>)</span> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">z</font></span>)</span> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <font color="Maroon" title="c3">z</font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="comseq_3.html#K8" title="COMSEQ_3:func.8">Sum</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="sin_cos.html#K6" title="SIN_COS:func.6">ExpSeq</a> </span>)</span></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">z</font> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p3">(<span class="default"><a href="comseq_3.html#K8" title="COMSEQ_3:func.8">Sum</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">z</font> <a href="sin_cos.html#K30" title="SIN_COS:func.30">P_dt</a> </span>)</span></span>)</span></span>)</span> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <font color="Maroon" title="c3">z</font></span>)</span>
<b>by </b><i><a class="ref" href="sin_cos.html#T62" target="_self" title="SIN_COS:th.62">Th62</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="comseq_3.html#K8" title="COMSEQ_3:func.8">Sum</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="sin_cos.html#K6" title="SIN_COS:func.6">ExpSeq</a> </span>)</span></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <font color="Maroon" title="c3">z</font></span>)</span> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">z</font> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p3">(<span class="default"><a href="comseq_3.html#K8" title="COMSEQ_3:func.8">Sum</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">z</font> <a href="sin_cos.html#K30" title="SIN_COS:func.30">P_dt</a> </span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p2">(<span class="default"><a href="comseq_3.html#K8" title="COMSEQ_3:func.8">Sum</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="sin_cos.html#K6" title="SIN_COS:func.6">ExpSeq</a> </span>)</span></span>)</span></span>)</span>

;<br/>
<b>hence </b><a NAME="E2:107"/>
<span class="p1">(<span class="default"><a href="comseq_3.html#K8" title="COMSEQ_3:func.8">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <font color="Maroon" title="c3">z</font></span>)</span> <a href="sin_cos.html#K6" title="SIN_COS:func.6">ExpSeq</a> </span>)</span></span>)</span> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <span class="p1">(<span class="default"><a href="comseq_3.html#K8" title="COMSEQ_3:func.8">Sum</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="sin_cos.html#K6" title="SIN_COS:func.6">ExpSeq</a> </span>)</span></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="comseq_3.html#K8" title="COMSEQ_3:func.8">Sum</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="sin_cos.html#K6" title="SIN_COS:func.6">ExpSeq</a> </span>)</span></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <font color="Maroon" title="c3">z</font></span>)</span> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">z</font> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p3">(<span class="default"><a href="comseq_3.html#K8" title="COMSEQ_3:func.8">Sum</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">z</font> <a href="sin_cos.html#K30" title="SIN_COS:func.30">P_dt</a> </span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p2">(<span class="default"><a href="comseq_3.html#K8" title="COMSEQ_3:func.8">Sum</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="sin_cos.html#K6" title="SIN_COS:func.6">ExpSeq</a> </span>)</span></span>)</span></span>)</span>
 ;<br/>


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