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<b>let </b><font color="Maroon">z2</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="complfld.html#K1" target="_self">F_Complex</a> ;<br/><b>let </b><font color="Maroon">z1</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="complfld.html#K1" target="_self">F_Complex</a> ;<br/>



<b>reconsider </b><font color="Maroon">z1'</font> = <font color="Maroon">z1</font>, <font color="Maroon">z2'</font> = <font color="Maroon">z2</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K2">COMPLEX</a>  <b>by </b><i/>;<br/>
<b>assume </b><a NAME="E2:21"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">z2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <a href="complfld.html#K1" target="_self">F_Complex</a> 
 ;<br/>

<b>assume </b><a NAME="E3:21"/><i><font color="Green">E43</font></i>: 
( <font color="Maroon">z1</font> <a href="group_1.html#K10">*</a> <font color="Maroon">z2</font> <a href="hidden.html#R1">=</a> the <a href="vectsp_1.html#U1">unity</a> of <a href="complfld.html#K1" target="_self">F_Complex</a>  or <font color="Maroon">z2</font> <a href="group_1.html#K10">*</a> <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> the <a href="vectsp_1.html#U1">unity</a> of <a href="complfld.html#K1" target="_self">F_Complex</a>  )
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:21_1"/>
( <font color="Maroon">z1</font> <a href="group_1.html#K10">*</a> <font color="Maroon">z2</font> <a href="hidden.html#R1">=</a> the <a href="vectsp_1.html#U1">unity</a> of <a href="complfld.html#K1" target="_self">F_Complex</a>  or <font color="Maroon">z2</font> <a href="group_1.html#K10">*</a> <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> the <a href="vectsp_1.html#U1">unity</a> of <a href="complfld.html#K1" target="_self">F_Complex</a>  )
 </span><b>by </b><i/>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_1"><b>suppose </b></a><a NAME="E1:21_1_1"/>
<font color="Maroon">z1</font> <a href="group_1.html#K10">*</a> <font color="Maroon">z2</font> <a href="hidden.html#R1">=</a> the <a href="vectsp_1.html#U1">unity</a> of <a href="complfld.html#K1" target="_self">F_Complex</a> 
 ;<br/><div class="add"><a NAME="E2:21_1_1"/><b>then </b>
<font color="Maroon">z1'</font> <a href="binop_2.html#K5">*</a> <font color="Maroon">z2'</font> <a href="hidden.html#R1">=</a> the <a href="vectsp_1.html#U1">unity</a> of <a href="complfld.html#K1" target="_self">F_Complex</a> 
 <b>by </b><i/>;<br/><a NAME="E3:21_1_1"/><b>then </b><i><font color="Green">E56</font></i>: 
<font color="Maroon">z1'</font> <a href="binop_2.html#K5">*</a> <font color="Maroon">z2'</font> <a href="hidden.html#R1">=</a>  <a href="complex1.html#K6">1r</a> 
 <b>by </b><i/>;<br/><a NAME="E4:21_1_1"/>
<font color="Maroon">z2</font> <a href="vectsp_1.html#K4">"</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">z2'</font> <a href="binop_2.html#K2">"</a> 
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E5:21_1_1"/>
<font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z2</font> <a href="vectsp_1.html#K4">"</a> 
 <b>by </b><i>, , , <a class="ref" href="complex1.html#D7">COMPLEX1:def 7</a>, <a class="ref" href="xcmplx_0.html#D7">XCMPLX_0:def 7</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_2"><b>suppose </b></a><a NAME="E1:21_1_2"/>
<font color="Maroon">z2</font> <a href="group_1.html#K10">*</a> <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> the <a href="vectsp_1.html#U1">unity</a> of <a href="complfld.html#K1" target="_self">F_Complex</a> 
 ;<br/><div class="add"><a NAME="E2:21_1_2"/><b>then </b>
<font color="Maroon">z2'</font> <a href="binop_2.html#K5">*</a> <font color="Maroon">z1'</font> <a href="hidden.html#R1">=</a> the <a href="vectsp_1.html#U1">unity</a> of <a href="complfld.html#K1" target="_self">F_Complex</a> 
 <b>by </b><i/>;<br/><a NAME="E3:21_1_2"/><b>then </b><i><font color="Green">E63</font></i>: 
<font color="Maroon">z2'</font> <a href="binop_2.html#K5">*</a> <font color="Maroon">z1'</font> <a href="hidden.html#R1">=</a>  <a href="complex1.html#K6">1r</a> 
 <b>by </b><i/>;<br/><a NAME="E4:21_1_2"/>
<font color="Maroon">z2</font> <a href="vectsp_1.html#K4">"</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">z2'</font> <a href="binop_2.html#K2">"</a> 
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E5:21_1_2"/>
<font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z2</font> <a href="vectsp_1.html#K4">"</a> 
 <b>by </b><i>, , , <a class="ref" href="complex1.html#D7">COMPLEX1:def 7</a>, <a class="ref" href="xcmplx_0.html#D7">XCMPLX_0:def 7</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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