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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K2">COMPLEX</a> ;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:1"/><i><font color="Green">E2</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="complex1.html#K5">0c</a> 
 <b>and </b><br/><a NAME="E2:1"/><i><font color="Green">E3</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="complex1.html#K5">0c</a> 
 ;<br/>

<b>thus </b><span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complex1.html#K12">"</a> </span>)</span> <a href="complex1.html#K11">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complex1.html#K12">"</a> </span>)</span></span>)</span></span><a href="complex1.html#K17">.|</a></span> = 
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K6">1r</a>  <a href="complex1.html#K13">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="complex1.html#K11">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complex1.html#K12">"</a> </span>)</span></span>)</span></span><a href="complex1.html#K17">.|</a></span>
<b>by </b><i><a class="ref" href="complex1.html#D7">COMPLEX1:def 7</a>, <a class="ref" href="xcmplx_1.html#T217">XCMPLX_1:217</a></i>
<br/>.= 
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K6">1r</a>  <a href="complex1.html#K13">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="complex1.html#K11">-</a> <span class="p3">(<span class="default"><a href="complex1.html#K6">1r</a>  <a href="complex1.html#K13">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="complex1.html#K17">.|</a></span>
<b>by </b><i><a class="ref" href="complex1.html#D7">COMPLEX1:def 7</a>, <a class="ref" href="xcmplx_1.html#T217">XCMPLX_1:217</a></i>
<br/>.= 
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K6">1r</a>  <a href="complex1.html#K13">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="complex1.html#K8">+</a> <span class="p3">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p4">(<span class="default"><a href="complex1.html#K6">1r</a>  <a href="complex1.html#K13">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span><a href="complex1.html#K17">.|</a></span>

<br/>.= 
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K6">1r</a>  <a href="complex1.html#K13">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="complex1.html#K8">+</a> <span class="p3">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p4">(<span class="default"><a href="complex1.html#K6">1r</a>  <a href="complex1.html#K9">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complex1.html#K12">"</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><a href="complex1.html#K17">.|</a></span>
<b>by </b><i><a class="ref" href="xcmplx_0.html#D9">XCMPLX_0:def 9</a></i>
<br/>.= 
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K6">1r</a>  <a href="complex1.html#K13">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="complex1.html#K8">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K10">-</a> <a href="complex1.html#K6">1r</a> </span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complex1.html#K12">"</a> </span>)</span></span>)</span></span>)</span></span><a href="complex1.html#K17">.|</a></span>

<br/>.= 
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K6">1r</a>  <a href="complex1.html#K13">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="complex1.html#K8">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K10">-</a> <a href="complex1.html#K6">1r</a> </span>)</span> <a href="complex1.html#K13">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="complex1.html#K17">.|</a></span>
<b>by </b><i><a class="ref" href="xcmplx_0.html#D9">XCMPLX_0:def 9</a></i>
<br/>.= 
<span class="p1"><a href="complex1.html#K17">|.</a><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#K6">1r</a>  <a href="complex1.html#K9">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="complex1.html#K8">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K10">-</a> <a href="complex1.html#K6">1r</a> </span>)</span> <a href="complex1.html#K9">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="complex1.html#K13">/</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complex1.html#K9">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span><a href="complex1.html#K17">.|</a></span>
<b>by </b><i><a class="txt" href="comseq_2.html#E1:1"><i><font color="Green">E2</font></i></a>, <a class="txt" href="comseq_2.html#E2:1"><i><font color="Green">E3</font></i></a>, <a class="ref" href="xcmplx_1.html#T117">XCMPLX_1:117</a></i>
<br/>.= 
<span class="p1"><a href="complex1.html#K17">|.</a><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#K6">1r</a>  <a href="complex1.html#K9">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="complex1.html#K11">-</a> <span class="p4">(<span class="default"><a href="complex1.html#K6">1r</a>  <a href="complex1.html#K9">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="complex1.html#K13">/</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complex1.html#K9">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span><a href="complex1.html#K17">.|</a></span>

<br/>.= 
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complex1.html#K11">-</a> <span class="p4">(<span class="default"><a href="complex1.html#K6">1r</a>  <a href="complex1.html#K9">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="complex1.html#K13">/</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complex1.html#K9">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span><a href="complex1.html#K17">.|</a></span>
<b>by </b><i><a class="ref" href="complex1.html#D7">COMPLEX1:def 7</a></i>
<br/>.= 
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complex1.html#K8">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K10">-</a> <a href="complex1.html#K6">1r</a> </span>)</span> <a href="complex1.html#K9">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="complex1.html#K13">/</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complex1.html#K9">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span><a href="complex1.html#K17">.|</a></span>

<br/>.= 
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complex1.html#K8">+</a> <span class="p4">(<span class="default"><a href="complex1.html#K10">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="complex1.html#K13">/</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complex1.html#K9">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span><a href="complex1.html#K17">.|</a></span>
<b>by </b><i><a class="ref" href="complex1.html#D7">COMPLEX1:def 7</a></i>
<br/>.= 
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K6">/</a> <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complex1.html#K9">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span>
<b>by </b><i><a class="ref" href="complex1.html#T153">COMPLEX1:153</a></i>
<br/>.= 
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="complex1.html#K17">.|</a></span></span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#T151">COMPLEX1:151</a></i>
<br/>.= 
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="complex1.html#K17">.|</a></span></span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#T138">COMPLEX1:138</a></i>
;<br/>


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