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<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_4_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:44_4_1_1"/>
( <font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K2">COMPLEX</a>  or  not <font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K2">COMPLEX</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_4_1_1_1"><b>suppose </b></a><a NAME="E1:44_4_1_1_1"/>
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K2">COMPLEX</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:44_4_1_1_1"/>
 <a href="quaterni.html#K16" target="_self">Im3</a> <font color="Maroon">z</font> is <a href="xreal_0.html#V1">real</a>
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_4_1_1_2"><b>suppose </b></a><a NAME="E1:44_4_1_1_2"/>
not <font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K2">COMPLEX</a> 
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">f</font> being   <a href="funct_2.html#NM1">Function</a> of 4, <a href="numbers.html#K1">REAL</a> <b> such that </b><br/><a NAME="E3:44_4_1_1_2"/>
<font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E4:44_4_1_1_2"/><i><font color="Green">E44</font></i>: 
 <a href="quaterni.html#K16" target="_self">Im3</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="seq_1.html#K2">.</a> 3
 <b>by </b><i/>;<br/><b>thus </b><a NAME="E5:44_4_1_1_2"/>
 <a href="quaterni.html#K16" target="_self">Im3</a> <font color="Maroon">z</font> is <a href="xreal_0.html#V1">real</a>
 <b>by </b><i/>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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