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<b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="complfld.html#K1">F_Complex</a> , <font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="complfld.html#K1">F_Complex</a> ;<br/>

<b>assume </b><a NAME="E1:9"/><i><font color="Green">E30</font></i>: 
 <a href="complex1.html#K4">Im</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 0
 ;<br/>

<b>hence </b> <a href="complex1.html#K3">Re</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K10">*</a> <font color="Maroon">b</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default">0 <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">b</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="hahnban1.html#T17">HAHNBAN1:17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">b</font></span>)</span>

;<br/><br/>

<b>thus </b> <a href="complex1.html#K4">Im</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K10">*</a> <font color="Maroon">b</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">b</font></span>)</span> <a href="real_1.html#K4">*</a> 0</span>)</span>
<b>by </b><i>, <a class="ref" href="hahnban1.html#T17">HAHNBAN1:17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">a</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">b</font></span>)</span>

;<br/>


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