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

<a NAME="E1:61"/>
(  <a href="complex1.html#K3" target="_self">Re</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complex1.html#K15" target="_self">*'</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="complex1.html#K4" target="_self">Im</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complex1.html#K15" target="_self">*'</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="complex1.html#T112" target="_self">Th112</a></i>;<br/>
<b>hence </b><a NAME="E2:61"/>
(  <a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0 implies <font color="Maroon">c<sub>1</sub></font> <a href="complex1.html#K15" target="_self">*'</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="ref" href="complex1.html#T9" target="_self">Th9</a></i>;<br/>


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