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<b>let </b><font color="Maroon" title="c1">z1</font>, <font color="Maroon" title="c2">z2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> ;<br/>



<b>reconsider </b><font color="Maroon" title="c3">z1'</font> = <font color="Maroon" title="c1">z1</font>, <font color="Maroon" title="c4">z2'</font> = <font color="Maroon" title="c2">z2</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" target="_self" title="COMPLFLD:def.1">Def1</a></i>;<br/>
<b>assume </b><a NAME="E2:26"/><i><font color="Green" title="E12">A1</font></i>: 
<font color="Maroon" title="c1">z1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> 
 ;<br/>

<a NAME="E3:26"/><b>then </b><i><font color="Green" title="E13">A2</font></i>: 
<font color="Maroon" title="c1">z1</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z1'</font> <a href="binop_2.html#K2" title="BINOP_2:func.2">"</a> 
 
<b>by </b><i><a class="ref" href="complfld.html#T7" target="_self" title="COMPLFLD:th.7">Th7</a></i>;<br/>
<b>assume </b><a NAME="E4:26"/><i><font color="Green" title="E14">A3</font></i>: 
<font color="Maroon" title="c2">z2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> 
 ;<br/>

<a NAME="E5:26"/><b>then </b><i><font color="Green" title="E15">A4</font></i>: 
<font color="Maroon" title="c2">z2</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">z2'</font> <a href="binop_2.html#K2" title="BINOP_2:func.2">"</a> 
 
<b>by </b><i><a class="ref" href="complfld.html#T7" target="_self" title="COMPLFLD:th.7">Th7</a></i>;<br/>
<a NAME="E6:26"/><i><font color="Green" title="E16">A5</font></i>: 
<font color="Maroon" title="c1">z1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <font color="Maroon" title="c2">z2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z1'</font> <a href="binop_2.html#K3" title="BINOP_2:func.3">+</a> <font color="Maroon" title="c4">z2'</font>
 
<b>by </b><i><a class="ref" href="complfld.html#T3" target="_self" title="COMPLFLD:th.3">Th3</a></i>;<br/>
<a NAME="E7:26"/><i><font color="Green" title="E17">A6</font></i>: 
<font color="Maroon" title="c1">z1</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c2">z2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> 
 
<b>by </b><i><a class="txt" href="complfld.html#E2:26"><i><font color="Green" title="E12">A1</font></i></a>, <a class="txt" href="complfld.html#E4:26"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="vectsp_1.html#T44" title="VECTSP_1:th.44">VECTSP_1:44</a></i>;<br/>
<a NAME="E8:26"/>
<font color="Maroon" title="c1">z1</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c2">z2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z1'</font> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <font color="Maroon" title="c4">z2'</font>
 
<b>by </b><i><a class="ref" href="complfld.html#T6" target="_self" title="COMPLFLD:th.6">Th6</a></i>;<br/>
<a NAME="E9:26"/><b>then </b><i><font color="Green" title="E18">A7</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">z1</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c2">z2</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">z1'</font> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <font color="Maroon" title="c4">z2'</font></span>)</span> <a href="binop_2.html#K2" title="BINOP_2:func.2">"</a> 
 
<b>by </b><i><a class="txt" href="complfld.html#E7:26"><i><font color="Green" title="E17">A6</font></i></a>, <a class="ref" href="complfld.html#T7" target="_self" title="COMPLFLD:th.7">Th7</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c1">z1</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">z2</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">z1'</font> <a href="binop_2.html#K2" title="BINOP_2:func.2">"</a> </span>)</span> <a href="binop_2.html#K3" title="BINOP_2:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">z2'</font> <a href="binop_2.html#K2" title="BINOP_2:func.2">"</a> </span>)</span>
<b>by </b><i><a class="txt" href="complfld.html#E3:26"><i><font color="Green" title="E13">A2</font></i></a>, <a class="txt" href="complfld.html#E5:26"><i><font color="Green" title="E15">A4</font></i></a>, <a class="ref" href="complfld.html#T3" target="_self" title="COMPLFLD:th.3">Th3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">z1'</font> <a href="binop_2.html#K3" title="BINOP_2:func.3">+</a> <font color="Maroon" title="c4">z2'</font></span>)</span> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">z1'</font> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <font color="Maroon" title="c4">z2'</font></span>)</span> <a href="binop_2.html#K2" title="BINOP_2:func.2">"</a> </span>)</span>
<b>by </b><i><a class="txt" href="complfld.html#E2:26"><i><font color="Green" title="E12">A1</font></i></a>, <a class="txt" href="complfld.html#E4:26"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="complfld.html#T9" target="_self" title="COMPLFLD:th.9">Th9</a>, <a class="ref" href="xcmplx_1.html#T213" title="XCMPLX_1:th.213">XCMPLX_1:213</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">z1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <font color="Maroon" title="c2">z2</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">z1</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c2">z2</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span>
<b>by </b><i><a class="txt" href="complfld.html#E6:26"><i><font color="Green" title="E16">A5</font></i></a>, <a class="txt" href="complfld.html#E9:26"><i><font color="Green" title="E18">A7</font></i></a>, <a class="ref" href="complfld.html#T6" target="_self" title="COMPLFLD:th.6">Th6</a></i>
;<br/>


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