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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>let </b><font color="Maroon">W</font> be    <a href="clvect_1.html#M1" target="_self">Subspace</a> of <font color="Maroon">V</font>;<br/>





<a NAME="E1:95"/><i><font color="Green">E28</font></i>: 
( ( <font color="Maroon">v</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W</font> implies <span class="p1">(<span class="default"><a href="complex1.html#K10">-</a> <a href="complex1.html#K6">1r</a> </span>)</span> <a href="clvect_1.html#K1" target="_self">*</a> <font color="Maroon">v</font> <a href="hidden.html#R2">in</a> <font color="Maroon">v</font> <a href="clvect_1.html#K4" target="_self">+</a> <font color="Maroon">W</font> ) &amp; <span class="p1">(<span class="default"><a href="complex1.html#K10">-</a> <a href="complex1.html#K6">1r</a> </span>)</span> <a href="clvect_1.html#K1" target="_self">*</a> <font color="Maroon">v</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K5">-</a> <font color="Maroon">v</font> )
 
<b>by </b><i>, <a class="ref" href="clvect_1.html#T11" target="_self">Th11</a></i>;<br/>
<a NAME="E2:95"/><i><font color="Green">E31</font></i>: 
(  <a href="complex1.html#K3">Re</a> <span class="p1">(<span class="default"><a href="complex1.html#K10">-</a> <a href="complex1.html#K6">1r</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#K3">Re</a> <a href="complex1.html#K6">1r</a> </span>)</span> &amp;  <a href="complex1.html#K4">Im</a> <span class="p1">(<span class="default"><a href="complex1.html#K10">-</a> <a href="complex1.html#K6">1r</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">Im</a> <a href="complex1.html#K6">1r</a> </span>)</span> )
 
<b>by </b><i><a class="ref" href="complex1.html#T34">COMPLEX1:34</a></i>;<br/>
<a NAME="E3:95"/>
(  <a href="complex1.html#K10">-</a> <a href="complex1.html#K6">1r</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="complex1.html#K6">1r</a>  &amp; <span class="p1">(<span class="default"><a href="complex1.html#K10">-</a> <a href="complex1.html#K6">1r</a> </span>)</span> <a href="clvect_1.html#K1" target="_self">*</a> <font color="Maroon">v</font> <a href="hidden.html#R2">in</a> <font color="Maroon">v</font> <a href="clvect_1.html#K4" target="_self">+</a> <font color="Maroon">W</font> implies <font color="Maroon">v</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W</font> )
 
<b>by </b><i><a class="ref" href="clvect_1.html#T10" target="_self">Th10</a></i>;<br/>
<b>hence </b><a NAME="E4:95"/>
(  <a href="rlvect_1.html#K5">-</a> <font color="Maroon">v</font> <a href="hidden.html#R2">in</a> <font color="Maroon">v</font> <a href="clvect_1.html#K4" target="_self">+</a> <font color="Maroon">W</font> iff <font color="Maroon">v</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W</font> )
 <b>by </b><i><a class="txt" href="clvect_1.html#E17"><i><font color="Green">Lemma61</font></i></a>, , <a class="ref" href="complex1.html#T15">COMPLEX1:15</a></i>;<br/>


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