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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="xcmplx_0.html#V1">complex</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<b>assume </b><a NAME="E1:54"/>
<font color="Maroon">c<sub>1</sub></font> <a href="complex1.html#K15" target="_self">*'</a>  <a href="hidden.html#R1">=</a> 0
 ;<br/>

<b>then </b>0 = 
<span class="p1">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</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>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7" target="_self">&lt;i&gt;</a> </span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <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></span>)</span> <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7" target="_self">&lt;i&gt;</a> </span>)</span>

;<br/>
<a NAME="E3:54"/><b>then </b>
(  <a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0 &amp;  <a href="real_1.html#K1">-</a> <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>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 0 )
 
<b>by </b><i><a class="ref" href="complex1.html#T28" target="_self">Th28</a>, <a class="ref" href="complex1.html#T12" target="_self">Th12</a></i>;<br/>
<b>hence </b><a NAME="E4:54"/>
(  <a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="complex1.html#K3" target="_self">Re</a> 0 &amp;  <a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="complex1.html#K4" target="_self">Im</a> 0 )
 <b>by </b><i><a class="txt" href="complex1.html#E23"><i><font color="Green">Lemma11</font></i></a>, <a class="txt" href="complex1.html#E12"><i><font color="Green">Lemma8</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="complex1.html#D5" target="_self">COMPLEX1:def 5</a><br/>


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