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<font color="Maroon">z1</font> <a href="quaterni.html#K9" target="_self">-</a> <font color="Maroon">z2</font> = 
<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="quaterni.html#K17" target="_self">Rea</a> <font color="Maroon">z1</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><a href="quaterni.html#K17" target="_self">Rea</a> <span class="p5">(<span class="default"><a href="quaterni.html#K28" target="_self">-</a> <font color="Maroon">z2</font></span>)</span></span>)</span></span>)</span> <a href="quaterni.html#K23" target="_self">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="quaterni.html#K18" target="_self">Im1</a> <font color="Maroon">z1</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><a href="quaterni.html#K18" target="_self">Im1</a> <span class="p0">(<span class="default"><a href="quaterni.html#K28" target="_self">-</a> <font color="Maroon">z2</font></span>)</span></span>)</span></span>)</span> <a href="quaterni.html#K25" target="_self">*</a> <a href="xcmplx_0.html#K1">&lt;i&gt;</a> </span>)</span></span>)</span> <a href="quaterni.html#K26" target="_self">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="quaterni.html#K19" target="_self">Im2</a> <font color="Maroon">z1</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><a href="quaterni.html#K19" target="_self">Im2</a> <span class="p5">(<span class="default"><a href="quaterni.html#K28" target="_self">-</a> <font color="Maroon">z2</font></span>)</span></span>)</span></span>)</span> <a href="quaterni.html#K25" target="_self">*</a> <a href="quaterni.html#K11" target="_self">&lt;j&gt;</a> </span>)</span></span>)</span> <a href="quaterni.html#K26" target="_self">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quaterni.html#K20" target="_self">Im3</a> <font color="Maroon">z1</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><a href="quaterni.html#K20" target="_self">Im3</a> <span class="p4">(<span class="default"><a href="quaterni.html#K28" target="_self">-</a> <font color="Maroon">z2</font></span>)</span></span>)</span></span>)</span> <a href="quaterni.html#K25" target="_self">*</a> <a href="quaterni.html#K12" target="_self">&lt;k&gt;</a> </span>)</span>
<b>by </b><i/>
<br/>.= 
<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="quaterni.html#K17" target="_self">Rea</a> <font color="Maroon">z1</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><a href="quaterni.html#K17" target="_self">Rea</a> <font color="Maroon">z2</font></span>)</span></span>)</span></span>)</span> <a href="quaterni.html#K23" target="_self">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="quaterni.html#K18" target="_self">Im1</a> <font color="Maroon">z1</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><a href="quaterni.html#K18" target="_self">Im1</a> <span class="p0">(<span class="default"><a href="quaterni.html#K28" target="_self">-</a> <font color="Maroon">z2</font></span>)</span></span>)</span></span>)</span> <a href="quaterni.html#K25" target="_self">*</a> <a href="xcmplx_0.html#K1">&lt;i&gt;</a> </span>)</span></span>)</span> <a href="quaterni.html#K26" target="_self">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="quaterni.html#K19" target="_self">Im2</a> <font color="Maroon">z1</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><a href="quaterni.html#K19" target="_self">Im2</a> <span class="p5">(<span class="default"><a href="quaterni.html#K28" target="_self">-</a> <font color="Maroon">z2</font></span>)</span></span>)</span></span>)</span> <a href="quaterni.html#K25" target="_self">*</a> <a href="quaterni.html#K11" target="_self">&lt;j&gt;</a> </span>)</span></span>)</span> <a href="quaterni.html#K26" target="_self">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quaterni.html#K20" target="_self">Im3</a> <font color="Maroon">z1</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><a href="quaterni.html#K20" target="_self">Im3</a> <span class="p4">(<span class="default"><a href="quaterni.html#K28" target="_self">-</a> <font color="Maroon">z2</font></span>)</span></span>)</span></span>)</span> <a href="quaterni.html#K25" target="_self">*</a> <a href="quaterni.html#K12" target="_self">&lt;k&gt;</a> </span>)</span>
<b>by </b><i/>
<br/>.= 
<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="quaterni.html#K17" target="_self">Rea</a> <font color="Maroon">z1</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><a href="quaterni.html#K17" target="_self">Rea</a> <font color="Maroon">z2</font></span>)</span></span>)</span></span>)</span> <a href="quaterni.html#K23" target="_self">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="quaterni.html#K18" target="_self">Im1</a> <font color="Maroon">z1</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><a href="quaterni.html#K18" target="_self">Im1</a> <font color="Maroon">z2</font></span>)</span></span>)</span> <a href="quaterni.html#K25" target="_self">*</a> <a href="xcmplx_0.html#K1">&lt;i&gt;</a> </span>)</span></span>)</span> <a href="quaterni.html#K26" target="_self">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="quaterni.html#K19" target="_self">Im2</a> <font color="Maroon">z1</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><a href="quaterni.html#K19" target="_self">Im2</a> <span class="p5">(<span class="default"><a href="quaterni.html#K28" target="_self">-</a> <font color="Maroon">z2</font></span>)</span></span>)</span></span>)</span> <a href="quaterni.html#K25" target="_self">*</a> <a href="quaterni.html#K11" target="_self">&lt;j&gt;</a> </span>)</span></span>)</span> <a href="quaterni.html#K26" target="_self">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quaterni.html#K20" target="_self">Im3</a> <font color="Maroon">z1</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><a href="quaterni.html#K20" target="_self">Im3</a> <span class="p4">(<span class="default"><a href="quaterni.html#K28" target="_self">-</a> <font color="Maroon">z2</font></span>)</span></span>)</span></span>)</span> <a href="quaterni.html#K25" target="_self">*</a> <a href="quaterni.html#K12" target="_self">&lt;k&gt;</a> </span>)</span>
<b>by </b><i/>
<br/>.= 
<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="quaterni.html#K17" target="_self">Rea</a> <font color="Maroon">z1</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><a href="quaterni.html#K17" target="_self">Rea</a> <font color="Maroon">z2</font></span>)</span></span>)</span></span>)</span> <a href="quaterni.html#K23" target="_self">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="quaterni.html#K18" target="_self">Im1</a> <font color="Maroon">z1</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><a href="quaterni.html#K18" target="_self">Im1</a> <font color="Maroon">z2</font></span>)</span></span>)</span> <a href="quaterni.html#K25" target="_self">*</a> <a href="xcmplx_0.html#K1">&lt;i&gt;</a> </span>)</span></span>)</span> <a href="quaterni.html#K26" target="_self">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="quaterni.html#K19" target="_self">Im2</a> <font color="Maroon">z1</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><a href="quaterni.html#K19" target="_self">Im2</a> <font color="Maroon">z2</font></span>)</span></span>)</span></span>)</span> <a href="quaterni.html#K25" target="_self">*</a> <a href="quaterni.html#K11" target="_self">&lt;j&gt;</a> </span>)</span></span>)</span> <a href="quaterni.html#K26" target="_self">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quaterni.html#K20" target="_self">Im3</a> <font color="Maroon">z1</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><a href="quaterni.html#K20" target="_self">Im3</a> <span class="p4">(<span class="default"><a href="quaterni.html#K28" target="_self">-</a> <font color="Maroon">z2</font></span>)</span></span>)</span></span>)</span> <a href="quaterni.html#K25" target="_self">*</a> <a href="quaterni.html#K12" target="_self">&lt;k&gt;</a> </span>)</span>
<b>by </b><i/>
<br/>.= 
<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="quaterni.html#K17" target="_self">Rea</a> <font color="Maroon">z1</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><a href="quaterni.html#K17" target="_self">Rea</a> <font color="Maroon">z2</font></span>)</span></span>)</span> <a href="quaterni.html#K23" target="_self">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="quaterni.html#K18" target="_self">Im1</a> <font color="Maroon">z1</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><a href="quaterni.html#K18" target="_self">Im1</a> <font color="Maroon">z2</font></span>)</span></span>)</span> <a href="quaterni.html#K25" target="_self">*</a> <a href="xcmplx_0.html#K1">&lt;i&gt;</a> </span>)</span></span>)</span> <a href="quaterni.html#K26" target="_self">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="quaterni.html#K19" target="_self">Im2</a> <font color="Maroon">z1</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><a href="quaterni.html#K19" target="_self">Im2</a> <font color="Maroon">z2</font></span>)</span></span>)</span> <a href="quaterni.html#K25" target="_self">*</a> <a href="quaterni.html#K11" target="_self">&lt;j&gt;</a> </span>)</span></span>)</span> <a href="quaterni.html#K26" target="_self">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quaterni.html#K20" target="_self">Im3</a> <font color="Maroon">z1</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><a href="quaterni.html#K20" target="_self">Im3</a> <font color="Maroon">z2</font></span>)</span></span>)</span> <a href="quaterni.html#K25" target="_self">*</a> <a href="quaterni.html#K12" target="_self">&lt;k&gt;</a> </span>)</span>
<b>by </b><i/>
;<br/>
<b>hence </b><a NAME="E2:85_1_1"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of  <a href="quaterni.html#K1" target="_self">QUATERNION</a>  holds <br/> ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">z1</font> <a href="quaterni.html#K9" target="_self">-</a> <font color="Maroon">z2</font> iff <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</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="quaterni.html#K17" target="_self">Rea</a> <font color="Maroon">z1</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><a href="quaterni.html#K17" target="_self">Rea</a> <font color="Maroon">z2</font></span>)</span></span>)</span> <a href="quaterni.html#K23" target="_self">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="quaterni.html#K18" target="_self">Im1</a> <font color="Maroon">z1</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><a href="quaterni.html#K18" target="_self">Im1</a> <font color="Maroon">z2</font></span>)</span></span>)</span> <a href="quaterni.html#K25" target="_self">*</a> <a href="xcmplx_0.html#K1">&lt;i&gt;</a> </span>)</span></span>)</span> <a href="quaterni.html#K26" target="_self">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="quaterni.html#K19" target="_self">Im2</a> <font color="Maroon">z1</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><a href="quaterni.html#K19" target="_self">Im2</a> <font color="Maroon">z2</font></span>)</span></span>)</span> <a href="quaterni.html#K25" target="_self">*</a> <a href="quaterni.html#K11" target="_self">&lt;j&gt;</a> </span>)</span></span>)</span> <a href="quaterni.html#K26" target="_self">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quaterni.html#K20" target="_self">Im3</a> <font color="Maroon">z1</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><a href="quaterni.html#K20" target="_self">Im3</a> <font color="Maroon">z2</font></span>)</span></span>)</span> <a href="quaterni.html#K25" target="_self">*</a> <a href="quaterni.html#K12" target="_self">&lt;k&gt;</a> </span>)</span> )
 ;<br/>


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