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<b>let </b><font color="Maroon">V</font> be   <a href="clvect_1.html#NM2">ComplexLinearSpace</a>;<br/><b>let </b><font color="Maroon">v</font> be   <a href="clvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/>



<b>assume </b><a NAME="E1:13"/>
<font color="Maroon">v</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K5">-</a> <font color="Maroon">v</font>
 ;<br/>

<b>then </b><i><font color="Green">E28</font></i>:  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font> = 
<font color="Maroon">v</font> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">v</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T28">RLVECT_1:28</a></i>
<br/>.= 
<font color="Maroon">v</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">v</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T30">RLVECT_1:30</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="complex1.html#K6">1r</a>  <a href="clvect_1.html#K1" target="_self">*</a> <font color="Maroon">v</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">v</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="complex1.html#K6">1r</a>  <a href="clvect_1.html#K1" target="_self">*</a> <font color="Maroon">v</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="complex1.html#K6">1r</a>  <a href="clvect_1.html#K1" target="_self">*</a> <font color="Maroon">v</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="complex1.html#K6">1r</a>  <a href="complex1.html#K8">+</a> <a href="complex1.html#K6">1r</a> </span>)</span> <a href="clvect_1.html#K1" target="_self">*</a> <font color="Maroon">v</font>
<b>by </b><i/>
;<br/>
<i><font color="Green">E31</font></i>:  <a href="complex1.html#K3">Re</a> <span class="p1">(<span class="default"><a href="complex1.html#K6">1r</a>  <a href="complex1.html#K8">+</a> <a href="complex1.html#K6">1r</a> </span>)</span> = 
1 <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <a href="complex1.html#K6">1r</a> </span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#T15">COMPLEX1:15</a>, <a class="ref" href="complex1.html#T19">COMPLEX1:19</a></i>
<br/>.= 
2
<b>by </b><i><a class="ref" href="complex1.html#T15">COMPLEX1:15</a></i>
;<br/>
 <a href="complex1.html#K4">Im</a> <span class="p1">(<span class="default"><a href="complex1.html#K6">1r</a>  <a href="complex1.html#K8">+</a> <a href="complex1.html#K6">1r</a> </span>)</span> = 
0 <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="complex1.html#K4">Im</a> <a href="complex1.html#K6">1r</a> </span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#T15">COMPLEX1:15</a>, <a class="ref" href="complex1.html#T19">COMPLEX1:19</a></i>
<br/>.= 
0
<b>by </b><i><a class="ref" href="complex1.html#T15">COMPLEX1:15</a></i>
;<br/>
<a NAME="E5:13"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p3">(<span class="default"><a href="complex1.html#K6">1r</a>  <a href="complex1.html#K8">+</a> <a href="complex1.html#K6">1r</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </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#K4">Im</a> <span class="p3">(<span class="default"><a href="complex1.html#K6">1r</a>  <a href="complex1.html#K8">+</a> <a href="complex1.html#K6">1r</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i>, <a class="ref" href="square_1.html#T60">SQUARE_1:60</a>, <a class="ref" href="square_1.html#T74">SQUARE_1:74</a></i>;<br/>
<a NAME="E6:13"/><b>then </b>
<a href="complex1.html#K6">1r</a>  <a href="complex1.html#K8">+</a> <a href="complex1.html#K6">1r</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="complex1.html#K5">0c</a> 
 
<b>by </b><i><a class="ref" href="complex1.html#T13">COMPLEX1:13</a></i>;<br/>
<b>hence </b><a NAME="E7:13"/>
<font color="Maroon">v</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font>
 <b>by </b><i>, </i>;<br/>


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