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<b>let </b><font color="Maroon">z</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="complfld.html#K1">F_Complex</a> ;<br/>

<b>assume </b><a NAME="E1:6"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">z</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <a href="complfld.html#K1">F_Complex</a> 
 ;<br/>

<b>reconsider </b><font color="Maroon">b</font> = <font color="Maroon">z</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K2">COMPLEX</a>  <b>by </b><i><a class="ref" href="complfld.html#D1">COMPLFLD:def 1</a></i>;<br/>
<b>set </b><font color="Maroon">a</font> = <span class="p1"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">z</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3"><a href="complfld.html#K3">|.</a><span class="default"><font color="Maroon">z</font></span><a href="complfld.html#K3">.|</a></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">Im</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3"><a href="complfld.html#K3">|.</a><span class="default"><font color="Maroon">z</font></span><a href="complfld.html#K3">.|</a></span></span>)</span></span><a href="hahnban1.html#K1">**]</a></span>;<br/>
<b>set </b><font color="Maroon">a1</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">z</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2"><a href="complfld.html#K3">|.</a><span class="default"><font color="Maroon">z</font></span><a href="complfld.html#K3">.|</a></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"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3"><a href="complfld.html#K3">|.</a><span class="default"><font color="Maroon">z</font></span><a href="complfld.html#K3">.|</a></span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7">&lt;i&gt;</a> </span>)</span>;<br/>
<a NAME="E3:6"/><i><font color="Green">E31</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">z</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2"><a href="complfld.html#K3">|.</a><span class="default"><font color="Maroon">z</font></span><a href="complfld.html#K3">.|</a></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"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3"><a href="complfld.html#K3">|.</a><span class="default"><font color="Maroon">z</font></span><a href="complfld.html#K3">.|</a></span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7">&lt;i&gt;</a> </span>)</span> <a href="hidden.html#R1">=</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">Re</a> <font color="Maroon">z</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3"><a href="complfld.html#K3">|.</a><span class="default"><font color="Maroon">z</font></span><a href="complfld.html#K3">.|</a></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">Im</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3"><a href="complfld.html#K3">|.</a><span class="default"><font color="Maroon">z</font></span><a href="complfld.html#K3">.|</a></span></span>)</span></span><a href="arytm_0.html#K5">*]</a></span>
 
<b>by </b><i><a class="ref" href="complex1.html#T27">COMPLEX1:27</a></i>;<br/>
<a NAME="E4:6"/>
<span class="p1"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">z</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3"><a href="complfld.html#K3">|.</a><span class="default"><font color="Maroon">z</font></span><a href="complfld.html#K3">.|</a></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">Im</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3"><a href="complfld.html#K3">|.</a><span class="default"><font color="Maroon">z</font></span><a href="complfld.html#K3">.|</a></span></span>)</span></span><a href="hahnban1.html#K1">**]</a></span> <a href="group_1.html#K10">*</a> <font color="Maroon">z</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"><a href="complex1.html#K3">Re</a> <font color="Maroon">z</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3"><a href="complfld.html#K3">|.</a><span class="default"><font color="Maroon">z</font></span><a href="complfld.html#K3">.|</a></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">Im</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4"><a href="complfld.html#K3">|.</a><span class="default"><font color="Maroon">z</font></span><a href="complfld.html#K3">.|</a></span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7">&lt;i&gt;</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="complfld.html#T6">COMPLFLD:6</a></i>;<br/>
<b>hence </b><a NAME="E5:6"/>
( <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">z</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4"><a href="complfld.html#K3">|.</a><span class="default"><font color="Maroon">z</font></span><a href="complfld.html#K3">.|</a></span></span>)</span>,<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">Im</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4"><a href="complfld.html#K3">|.</a><span class="default"><font color="Maroon">z</font></span><a href="complfld.html#K3">.|</a></span></span>)</span></span><a href="hahnban1.html#K1">**]</a></span></span><a href="complfld.html#K3">.|</a></span> <a href="hidden.html#R1">=</a> 1 &amp;  <a href="complex1.html#K3">Re</a> <span class="p1">(<span class="default"><span class="p2"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">z</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4"><a href="complfld.html#K3">|.</a><span class="default"><font color="Maroon">z</font></span><a href="complfld.html#K3">.|</a></span></span>)</span>,<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">Im</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4"><a href="complfld.html#K3">|.</a><span class="default"><font color="Maroon">z</font></span><a href="complfld.html#K3">.|</a></span></span>)</span></span><a href="hahnban1.html#K1">**]</a></span> <a href="group_1.html#K10">*</a> <font color="Maroon">z</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><font color="Maroon">z</font></span><a href="complfld.html#K3">.|</a></span> &amp;  <a href="complex1.html#K4">Im</a> <span class="p1">(<span class="default"><span class="p2"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">z</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4"><a href="complfld.html#K3">|.</a><span class="default"><font color="Maroon">z</font></span><a href="complfld.html#K3">.|</a></span></span>)</span>,<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">Im</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4"><a href="complfld.html#K3">|.</a><span class="default"><font color="Maroon">z</font></span><a href="complfld.html#K3">.|</a></span></span>)</span></span><a href="hahnban1.html#K1">**]</a></span> <a href="group_1.html#K10">*</a> <font color="Maroon">z</font></span>)</span> <a href="hidden.html#R1">=</a> 0 )
 <b>by </b><i>, , <a class="ref" href="complfld.html#T9">COMPLFLD:9</a>, </i>;<br/>


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