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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/><b>let </b><font color="Maroon">r</font> be   <a href="real_1.html#NM1">Real</a>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:13"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">z</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>and </b><br/><a NAME="E2:13"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">z</font> <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"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">z</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K24">cos</a> <font color="Maroon">r</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">z</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K21">sin</a> <font color="Maroon">r</font></span>)</span></span>)</span></span><a href="arytm_0.html#K5">*]</a></span>
 <b>and </b><br/><a NAME="E3:13"/><i><font color="Green">E29</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">r</font>
 <b>and </b><br/><a NAME="E4:13"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">r</font> <a href="xxreal_0.html#R1">&lt;</a> 2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K35">PI</a> 
 ;<br/>

<a NAME="E5:13"/>
<font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">z</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="sin_cos.html#K24">cos</a> <font color="Maroon">r</font></span>)</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"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">z</font></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K21">sin</a> <font color="Maroon">r</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7">&lt;i&gt;</a> </span>)</span>
 
<b>by </b><i>, <a class="ref" href="complex1.html#T27">COMPLEX1:27</a></i>;<br/>
<b>hence </b><a NAME="E6:13"/>
<font color="Maroon">r</font> <a href="hidden.html#R1">=</a>  <a href="comptrig.html#K1">Arg</a> <font color="Maroon">z</font>
 <b>by </b><i>, , , <a class="ref" href="comptrig.html#D1">COMPTRIG:def 1</a></i>;<br/>


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