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<b>let </b><font color="Maroon">c<sub>5</sub></font> be  <a href="xcmplx_0.html#V1">complex</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/>



<b>thus </b> <a href="complex2.html#K3">Rotate</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> = 
<span class="p1"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K24">cos</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K21">sin</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="arytm_0.html#K5">*]</a></span>
<b>by </b><i><a class="ref" href="complex2.html#D4">COMPLEX2:def 4</a></i>
<br/>.= 
<span class="p1"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K24">cos</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span> <a href="real_1.html#K4">*</a> 1</span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p0">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K21">sin</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="arytm_0.html#K5">*]</a></span>
<b>by </b><i><a class="ref" href="complex2.html#T10">COMPLEX2:10</a></i>
<br/>.= 
<span class="p1"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K24">cos</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K21">sin</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><a href="comptrig.html#K1">Arg</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="arytm_0.html#K5">*]</a></span>
<b>by </b><i><a class="ref" href="complex2.html#T9">COMPLEX2:9</a></i>
<br/>.= 
 <a href="complex2.html#K3">Rotate</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="complex2.html#D4">COMPLEX2:def 4</a></i>
;<br/>


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