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<b>let </b><font color="Maroon" title="c1">z1</font>, <font color="Maroon" title="c2">z2</font> be    <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> ;<br/>



<a NAME="E1:12"/>
<span class="p1">(<span class="default"><a href="euclid_3.html#K1" title="EUCLID_3:func.1">cpx2euc</a> <font color="Maroon" title="c1">z1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p1">(<span class="default"><a href="euclid_3.html#K1" title="EUCLID_3:func.1">cpx2euc</a> <font color="Maroon" title="c2">z2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><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="c1">z1</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p3">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c2">z2</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c1">z1</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p3">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c2">z2</font></span>)</span></span>)</span></span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span>
 
<b>by </b><i><a class="ref" href="euclid.html#T60" title="EUCLID:th.60">EUCLID:60</a></i>;<br/>
<b>hence </b><a NAME="E2:12"/>
 <a href="euclid_3.html#K1" title="EUCLID_3:func.1">cpx2euc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z1</font> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <font color="Maroon" title="c2">z2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="euclid_3.html#K1" title="EUCLID_3:func.1">cpx2euc</a> <font color="Maroon" title="c1">z1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p1">(<span class="default"><a href="euclid_3.html#K1" title="EUCLID_3:func.1">cpx2euc</a> <font color="Maroon" title="c2">z2</font></span>)</span>
 <b>by </b><i><a class="ref" href="euclid_3.html#T10" target="_self" title="EUCLID_3:th.10">Th10</a></i>;<br/>


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