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

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:24_1"/><i><font color="Green">E23</font></i>: 
 <a href="complex1.html#K4">Im</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><a NAME="E2:24_1"/>
(  <a href="complex1.html#K3">Re</a> <font color="Maroon">z</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 or  <a href="complex1.html#K3">Re</a> <font color="Maroon">z</font> <a href="xxreal_0.html#R1">&lt;</a> 0 )
 ;<br/><a NAME="E3:24_1"/><b>then </b>
(  <a href="comptrig.html#K1">Arg</a> <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="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default">0 <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7">&lt;i&gt;</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0 or  <a href="comptrig.html#K1">Arg</a> <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="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default">0 <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7">&lt;i&gt;</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="sin_cos.html#K35">PI</a>  )
 <b>by </b><i><a class="ref" href="comptrig.html#T53">COMPTRIG:53</a>, <a class="ref" href="comptrig.html#T54">COMPTRIG:54</a></i>;<br/><b>hence </b><a NAME="E4:24_1"/>
(  <a href="comptrig.html#K1">Arg</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> 0 or  <a href="comptrig.html#K1">Arg</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="sin_cos.html#K35">PI</a>  )
 <b>by </b><i>, <a class="ref" href="complex1.html#T29">COMPLEX1:29</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:24"/>
(  <a href="comptrig.html#K1">Arg</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> 0 or  <a href="comptrig.html#K1">Arg</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="sin_cos.html#K35">PI</a>  )
 ;<br/>

<b>hence </b><a NAME="E3:24"/>
 <a href="complex1.html#K4">Im</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="complex2.html#T2" target="_self">Th2</a>, </i>;<br/>


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