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<b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="jordan24.html#K1" target="_self">Rotate</a> <span class="p2">(<span class="default"><span class="p3">(<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>5</sub></font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>6</sub></font> = 
<span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p3">(<span class="default"><a href="complex2.html#K3">Rotate</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K3">*</a> <a href="xcmplx_0.html#K1">&lt;i&gt;</a> </span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<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>5</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p3">(<span class="default"><a href="complex2.html#K3">Rotate</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K3">*</a> <a href="xcmplx_0.html#K1">&lt;i&gt;</a> </span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<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>5</sub></font></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span>
<b>by </b><i><a class="ref" href="jordan24.html#D3" target="_self">Def3</a></i>
<br/>.= 
<span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p3">(<span class="default"><a href="complex2.html#K3">Rotate</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K3">*</a> <a href="xcmplx_0.html#K1">&lt;i&gt;</a> </span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p3">(<span class="default"><a href="complex2.html#K3">Rotate</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K3">*</a> <a href="xcmplx_0.html#K1">&lt;i&gt;</a> </span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<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>5</sub></font></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span>
<b>by </b><i><a class="ref" href="jordan24.html#T5" target="_self">Th5</a></i>
<br/>.= 
<span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p3">(<span class="default"><a href="complex2.html#K3">Rotate</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K3">*</a> <a href="xcmplx_0.html#K1">&lt;i&gt;</a> </span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p3">(<span class="default"><a href="complex2.html#K3">Rotate</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K3">*</a> <a href="xcmplx_0.html#K1">&lt;i&gt;</a> </span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span>
<b>by </b><i><a class="ref" href="jordan24.html#T5" target="_self">Th5</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:12"/>
 <a href="jordan24.html#K1" target="_self">Rotate</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="funct_2.html#R2">=</a>  <a href="jordan24.html#K1" target="_self">Rotate</a> <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>5</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="jordan24.html#D3" target="_self">Def3</a></i>;<br/>


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