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<b>let </b><font color="Maroon" title="c1">V</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of  <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> ;<br/><b>let </b><font color="Maroon" title="c2">l</font> be   <a href="hahnban.html#NM3" title="HAHNBAN:NM.3">linear-Functional</a> of <span class="p1">(<span class="default"><a href="hahnban1.html#K10" title="HAHNBAN1:func.10">RealVS</a> <font color="Maroon" title="c1">V</font></span>)</span>;<br/>



<a NAME="E1:84"/><i><font color="Green" title="E39">A1</font></i>: 
 <a href="hahnban1.html#K16" title="HAHNBAN1:func.16">prodReIm</a> <font color="Maroon" title="c2">l</font> is <a href="hahnban1.html#V1" title="HAHNBAN1:attr.1">additive</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">y</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c1">V</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="hahnban1.html#D11" target="_self" title="HAHNBAN1:def.11">HAHNBAN1:def 11</a><br/>

<b>thus </b><span class="p1">(<span class="default"><a href="hahnban1.html#K16" title="HAHNBAN1:func.16">prodReIm</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c4">y</font></span>)</span> = 
<span class="p1"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c4">y</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="hahnban1.html#K15" title="HAHNBAN1:func.15">i-shift</a> <span class="p5">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c4">y</font></span>)</span></span>)</span></span>)</span></span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span>
<b>by </b><i><a class="ref" href="hahnban1.html#D28" target="_self" title="HAHNBAN1:def.28">Def28</a></i>
<br/>.= 
<span class="p1"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c4">y</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p4">(<span class="default"><a href="hahnban1.html#K2" title="HAHNBAN1:func.2">i_FC</a>  <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c4">y</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span>
<b>by </b><i><a class="ref" href="hahnban1.html#D27" target="_self" title="HAHNBAN1:def.27">Def27</a></i>
<br/>.= 
<span class="p1"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p4">(<span class="default"><a href="hahnban1.html#K2" title="HAHNBAN1:func.2">i_FC</a>  <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c4">y</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span>
<b>by </b><i><a class="ref" href="hahnban1.html#D17" target="_self" title="HAHNBAN1:def.17">Def17</a></i>
<br/>.= 
<span class="p1"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="hahnban1.html#K2" title="HAHNBAN1:func.2">i_FC</a>  <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p5">(<span class="default"><a href="hahnban1.html#K2" title="HAHNBAN1:func.2">i_FC</a>  <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c4">y</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D26" title="VECTSP_1:def.26">VECTSP_1:def 26</a></i>
<br/>.= 
<span class="p1"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p5">(<span class="default"><a href="hahnban1.html#K2" title="HAHNBAN1:func.2">i_FC</a>  <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p5">(<span class="default"><a href="hahnban1.html#K2" title="HAHNBAN1:func.2">i_FC</a>  <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c4">y</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span>
<b>by </b><i><a class="ref" href="hahnban1.html#D17" target="_self" title="HAHNBAN1:def.17">Def17</a></i>
<br/>.= 
<span class="p1"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font></span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p4">(<span class="default"><a href="hahnban1.html#K2" title="HAHNBAN1:func.2">i_FC</a>  <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span></span>)</span></span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font></span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p4">(<span class="default"><a href="hahnban1.html#K2" title="HAHNBAN1:func.2">i_FC</a>  <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c4">y</font></span>)</span></span>)</span></span>)</span></span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span>

<br/>.= 
<span class="p1"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font></span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="hahnban1.html#K15" title="HAHNBAN1:func.15">i-shift</a> <span class="p5">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span></span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font></span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p4">(<span class="default"><a href="hahnban1.html#K2" title="HAHNBAN1:func.2">i_FC</a>  <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c4">y</font></span>)</span></span>)</span></span>)</span></span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span>
<b>by </b><i><a class="ref" href="hahnban1.html#D27" target="_self" title="HAHNBAN1:def.27">Def27</a></i>
<br/>.= 
<span class="p1"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font></span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="hahnban1.html#K15" title="HAHNBAN1:func.15">i-shift</a> <span class="p5">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span></span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font></span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="hahnban1.html#K15" title="HAHNBAN1:func.15">i-shift</a> <span class="p5">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font></span>)</span></span>)</span></span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span>
<b>by </b><i><a class="ref" href="hahnban1.html#D27" target="_self" title="HAHNBAN1:def.27">Def27</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="hahnban1.html#K16" title="HAHNBAN1:func.16">prodReIm</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font></span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="hahnban1.html#K15" title="HAHNBAN1:func.15">i-shift</a> <span class="p5">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font></span>)</span></span>)</span></span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span>
<b>by </b><i><a class="ref" href="hahnban1.html#D28" target="_self" title="HAHNBAN1:def.28">Def28</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="hahnban1.html#K16" title="HAHNBAN1:func.16">prodReIm</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="hahnban1.html#K16" title="HAHNBAN1:func.16">prodReIm</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font></span>)</span>
<b>by </b><i><a class="ref" href="hahnban1.html#D28" target="_self" title="HAHNBAN1:def.28">Def28</a></i>
;<br/>


</div><b>end;</b></div>
<a NAME="E2:84"/>
 <a href="hahnban1.html#K16" title="HAHNBAN1:func.16">prodReIm</a> <font color="Maroon" title="c2">l</font> is <a href="hahnban1.html#V2" title="HAHNBAN1:attr.2">homogeneous</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">x</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c1">V</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="hahnban1.html#D12" target="_self" title="HAHNBAN1:def.12">HAHNBAN1:def 12</a><br/><b>let </b><font color="Maroon" title="c4">r</font> be   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Scalar</a> of ;<br/>



<b>reconsider </b><font color="Maroon" title="c5">r1</font> = <font color="Maroon" title="c4">r</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>  <b>by </b><i><a class="ref" href="complfld.html#D1" title="COMPLFLD:def.1">COMPLFLD:def 1</a></i>;<br/>
<b>set </b><font color="Maroon" title="c6">a</font> =  <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c5">r1</font>;<br/>
<b>set </b><font color="Maroon" title="c7">b</font> =  <a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c5">r1</font>;<br/>
<a NAME="E2:84_2"/><i><font color="Green" title="E40">A2</font></i>: 
<font color="Maroon" title="c5">r1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c5">r1</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c5">r1</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="complex1.html#T29" title="COMPLEX1:th.29">COMPLEX1:29</a></i>;<br/>
<i><font color="Green" title="E41">A3</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c5">r1</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c5">r1</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p4">(<span class="default"><a href="hahnban1.html#K2" title="HAHNBAN1:func.2">i_FC</a>  <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c5">r1</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c5">r1</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><a href="hahnban1.html#K2" title="HAHNBAN1:func.2">i_FC</a>  <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c5">r1</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c5">r1</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><a href="hahnban1.html#K2" title="HAHNBAN1:func.2">i_FC</a>  <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="hahnban1.html#D18" target="_self" title="HAHNBAN1:def.18">Def18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c5">r1</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<span class="p4">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c5">r1</font></span>)</span></span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="hahnban1.html#T29" target="_self" title="HAHNBAN1:th.29">Th29</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c5">r1</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<span class="p4">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c5">r1</font></span>)</span></span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="hahnban1.html#D17" target="_self" title="HAHNBAN1:def.17">Def17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c5">r1</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<span class="p4">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c5">r1</font></span>)</span></span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span></span>)</span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">x</font></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D26" title="VECTSP_1:def.26">VECTSP_1:def 26</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">r</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">x</font></span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#T29" title="COMPLEX1:th.29">COMPLEX1:29</a></i>
;<br/>
<i><font color="Green" title="E42">A4</font></i>: <font color="Maroon" title="c3">x</font> = 
<span class="p1">(<span class="default"><a href="hahnban1.html#K2" title="HAHNBAN1:func.2">i_FC</a>  <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><a href="hahnban1.html#K2" title="HAHNBAN1:func.2">i_FC</a>  <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p3">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">x</font>
<b>by </b><i><a class="ref" href="hahnban1.html#T8" target="_self" title="HAHNBAN1:th.8">Th8</a>, <a class="ref" href="hahnban1.html#T9" target="_self" title="HAHNBAN1:th.9">Th9</a>, <a class="ref" href="vectsp_1.html#D26" title="VECTSP_1:def.26">VECTSP_1:def 26</a></i>
<br/>.= 
<a href="hahnban1.html#K2" title="HAHNBAN1:func.2">i_FC</a>  <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <a href="hahnban1.html#K2" title="HAHNBAN1:func.2">i_FC</a> </span>)</span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">x</font></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D26" title="VECTSP_1:def.26">VECTSP_1:def 26</a></i>
;<br/>
<a NAME="E5:84_2"/><i><font color="Green" title="E43">A5</font></i>: 
 <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span>
 
<b>by </b><i><a class="ref" href="complfld.html#T4" title="COMPLFLD:th.4">COMPLFLD:4</a>, <a class="ref" href="complfld.html#T10" title="COMPLFLD:th.10">COMPLFLD:10</a></i>;<br/>
<i><font color="Green" title="E44">A6</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c5">r1</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p4">(<span class="default"><a href="hahnban1.html#K2" title="HAHNBAN1:func.2">i_FC</a>  <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c5">r1</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c5">r1</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p4">(<span class="default"><a href="hahnban1.html#K2" title="HAHNBAN1:func.2">i_FC</a>  <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c5">r1</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><a href="hahnban1.html#K2" title="HAHNBAN1:func.2">i_FC</a>  <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <a href="hahnban1.html#K2" title="HAHNBAN1:func.2">i_FC</a> </span>)</span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="hahnban1.html#E4:84_2"><i><font color="Green" title="E42">A4</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c5">r1</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <span class="p4">(<span class="default"><a href="hahnban1.html#K2" title="HAHNBAN1:func.2">i_FC</a>  <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p4">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c5">r1</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p4">(<span class="default"><a href="hahnban1.html#K2" title="HAHNBAN1:func.2">i_FC</a>  <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <a href="hahnban1.html#K2" title="HAHNBAN1:func.2">i_FC</a> </span>)</span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="hahnban1.html#D18" target="_self" title="HAHNBAN1:def.18">Def18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c5">r1</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <span class="p4">(<span class="default"><a href="hahnban1.html#K2" title="HAHNBAN1:func.2">i_FC</a>  <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p0">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c5">r1</font></span>)</span></span>)</span></span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <a href="hahnban1.html#K2" title="HAHNBAN1:func.2">i_FC</a> </span>)</span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="hahnban1.html#T29" target="_self" title="HAHNBAN1:th.29">Th29</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c5">r1</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <span class="p4">(<span class="default"><a href="hahnban1.html#K2" title="HAHNBAN1:func.2">i_FC</a>  <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p0">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c5">r1</font></span>)</span></span>)</span></span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p0">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span>)</span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <span class="p5">(<span class="default"><a href="hahnban1.html#K2" title="HAHNBAN1:func.2">i_FC</a>  <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D26" title="VECTSP_1:def.26">VECTSP_1:def 26</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c5">r1</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <span class="p4">(<span class="default"><a href="hahnban1.html#K2" title="HAHNBAN1:func.2">i_FC</a>  <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c5">r1</font></span>)</span></span>)</span></span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p5">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p0">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <span class="p4">(<span class="default"><a href="hahnban1.html#K2" title="HAHNBAN1:func.2">i_FC</a>  <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D26" title="VECTSP_1:def.26">VECTSP_1:def 26</a></i>
<br/>.= 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c5">r1</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <span class="p4">(<span class="default"><a href="hahnban1.html#K2" title="HAHNBAN1:func.2">i_FC</a>  <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<span class="p5">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c5">r1</font></span>)</span></span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <span class="p4">(<span class="default"><a href="hahnban1.html#K2" title="HAHNBAN1:func.2">i_FC</a>  <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="hahnban1.html#E5:84_2"><i><font color="Green" title="E43">A5</font></i></a></i>
<br/>.= 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c5">r1</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <span class="p4">(<span class="default"><a href="hahnban1.html#K2" title="HAHNBAN1:func.2">i_FC</a>  <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<span class="p5">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c5">r1</font></span>)</span></span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <span class="p4">(<span class="default"><a href="hahnban1.html#K2" title="HAHNBAN1:func.2">i_FC</a>  <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="hahnban1.html#D17" target="_self" title="HAHNBAN1:def.17">Def17</a></i>
<br/>.= 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c5">r1</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<span class="p5">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c5">r1</font></span>)</span></span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span></span>)</span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <span class="p3">(<span class="default"><a href="hahnban1.html#K2" title="HAHNBAN1:func.2">i_FC</a>  <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D26" title="VECTSP_1:def.26">VECTSP_1:def 26</a></i>
<br/>.= 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="hahnban1.html#K2" title="HAHNBAN1:func.2">i_FC</a>  <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c4">r</font></span>)</span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="hahnban1.html#E2:84_2"><i><font color="Green" title="E40">A2</font></i></a>, <a class="ref" href="vectsp_1.html#D26" title="VECTSP_1:def.26">VECTSP_1:def 26</a></i>
;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="hahnban1.html#K16" title="HAHNBAN1:func.16">prodReIm</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">r</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">x</font></span>)</span> = 
<span class="p1"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">r</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="hahnban1.html#K15" title="HAHNBAN1:func.15">i-shift</a> <span class="p5">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">r</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span></span>)</span></span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span>
<b>by </b><i><a class="ref" href="hahnban1.html#D28" target="_self" title="HAHNBAN1:def.28">Def28</a></i>
<br/>.= 
<span class="p1"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">r</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p4">(<span class="default"><a href="hahnban1.html#K2" title="HAHNBAN1:func.2">i_FC</a>  <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">r</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span>
<b>by </b><i><a class="ref" href="hahnban1.html#D27" target="_self" title="HAHNBAN1:def.27">Def27</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">r</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c5">r1</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p0">(<span class="default"><a href="hahnban1.html#K2" title="HAHNBAN1:func.2">i_FC</a>  <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c5">r1</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a> </span>)</span>
<b>by </b><i><a class="txt" href="hahnban1.html#E6:84_2"><i><font color="Green" title="E44">A6</font></i></a>, <a class="ref" href="vectsp_1.html#D26" title="VECTSP_1:def.26">VECTSP_1:def 26</a></i>
<br/>.= 
<font color="Maroon" title="c4">r</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font></span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p4">(<span class="default"><a href="hahnban1.html#K2" title="HAHNBAN1:func.2">i_FC</a>  <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span></span>)</span></span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span>
<b>by </b><i><a class="txt" href="hahnban1.html#E2:84_2"><i><font color="Green" title="E40">A2</font></i></a>, <a class="txt" href="hahnban1.html#E3:84_2"><i><font color="Green" title="E41">A3</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c4">r</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font></span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="hahnban1.html#K15" title="HAHNBAN1:func.15">i-shift</a> <span class="p5">(<span class="default"><a href="hahnban1.html#K13" title="HAHNBAN1:func.13">RtoC</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span></span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span>
<b>by </b><i><a class="ref" href="hahnban1.html#D27" target="_self" title="HAHNBAN1:def.27">Def27</a></i>
<br/>.= 
<font color="Maroon" title="c4">r</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="hahnban1.html#K16" title="HAHNBAN1:func.16">prodReIm</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font></span>)</span>
<b>by </b><i><a class="ref" href="hahnban1.html#D28" target="_self" title="HAHNBAN1:def.28">Def28</a></i>
;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:84"/>
 <a href="hahnban1.html#K16" title="HAHNBAN1:func.16">prodReIm</a> <font color="Maroon" title="c2">l</font> is   <a href="hahnban1.html#NM2" title="HAHNBAN1:NM.2">linear-Functional</a> of <font color="Maroon" title="c1">V</font>
 <b>by </b><i><a class="txt" href="hahnban1.html#E1:84"><i><font color="Green" title="E39">A1</font></i></a></i>;<br/>


</div>
