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<b>set </b><font color="Maroon">c<sub>3</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>;<br/>
<i><font color="Green">E48</font></i>:  <a href="complex1.html#K3" target="_self">Re</a> <span class="p1"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span><a href="arytm_0.html#K5">*]</a></span> = 
 <a href="complex1.html#K3" target="_self">Re</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7" target="_self">&lt;i&gt;</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="complex1.html#E47"><i><font color="Green">Lemma31</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#T28" target="_self">Th28</a></i>
;<br/>
<i><font color="Green">E49</font></i>:  <a href="complex1.html#K4" target="_self">Im</a> <span class="p1"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span><a href="arytm_0.html#K5">*]</a></span> = 
 <a href="complex1.html#K4" target="_self">Im</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7" target="_self">&lt;i&gt;</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="complex1.html#E47"><i><font color="Green">Lemma31</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#T28" target="_self">Th28</a></i>
;<br/>
<font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>2</sub></font> = 
<font color="Maroon">c<sub>1</sub></font> <a href="complex1.html#K9" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complex1.html#K12" target="_self">"</a> </span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_0.html#D9">XCMPLX_0:def 9</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7" target="_self">&lt;i&gt;</a> </span>)</span></span>)</span>

<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="complex1.html#K9" target="_self">*</a> <span class="p1"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span><a href="arytm_0.html#K5">*]</a></span>
<b>by </b><i><a class="txt" href="complex1.html#E47"><i><font color="Green">Lemma31</font></i></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">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p0">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p0">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span><a href="arytm_0.html#K5">*]</a></span>
<b>by </b><i><a class="txt" href="complex1.html#E1:48_1_1"><i><font color="Green">E48</font></i></a>, <a class="txt" href="complex1.html#E2:48_1_1"><i><font color="Green">E49</font></i></a>, <a class="txt" href="complex1.html#E42"><i><font color="Green">Lemma26</font></i></a></i>
<br/>.= 
<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="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</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="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p0">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7" target="_self">&lt;i&gt;</a> </span>)</span>
<b>by </b><i><a class="txt" href="complex1.html#E47"><i><font color="Green">Lemma31</font></i></a></i>
<br/>.= 
<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="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</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="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p0">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7" target="_self">&lt;i&gt;</a> </span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T77">XCMPLX_1:77</a></i>
<br/>.= 
<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="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</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"><span class="p5">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p0">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7" target="_self">&lt;i&gt;</a> </span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T77">XCMPLX_1:77</a></i>
<br/>.= 
<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="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</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"><span class="p5">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p0">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7" target="_self">&lt;i&gt;</a> </span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T77">XCMPLX_1:77</a></i>
<br/>.= 
<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="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</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"><span class="p5">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p0">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7" target="_self">&lt;i&gt;</a> </span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T77">XCMPLX_1:77</a></i>
<br/>.= 
<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="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</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"><span class="p5">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p0">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7" target="_self">&lt;i&gt;</a> </span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T121">XCMPLX_1:121</a></i>
<br/>.= 
<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="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</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="real_1.html#K1">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p0">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7" target="_self">&lt;i&gt;</a> </span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T63">XCMPLX_1:63</a></i>
<br/>.= 
<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="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</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"><span class="p5">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7" target="_self">&lt;i&gt;</a> </span>)</span>

;<br/>
<b>hence </b><a NAME="E4:48_1_1"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K2">COMPLEX</a>  holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>2</sub></font> iff <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</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="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</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"><span class="p5">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7" target="_self">&lt;i&gt;</a> </span>)</span> )
 ;<br/>


</div>
