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<b>reconsider </b><font color="Maroon">z'</font> = <span class="p1"><a href="quaterni.html#K6" target="_self">[*</a><span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">v</font></span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">w</font></span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">x</font></span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">y</font></span>)</span></span><a href="quaterni.html#K6" target="_self">*]</a></span> as  <a href="quaterni.html#V1" target="_self">quaternion</a>  <a href="ordinal1.html#NM1" target="_self">number</a>  ;<br/>
<b>take </b>
<font color="Maroon">z'</font>
;<br/>

<a NAME="E2:29_1_1"/>
( 0 <a href="hidden.html#R1">=</a> <font color="Maroon">v</font> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">v</font></span>)</span> &amp; 0 <a href="hidden.html#R1">=</a> <font color="Maroon">w</font> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">w</font></span>)</span> &amp; 0 <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">x</font></span>)</span> &amp; 0 <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">y</font></span>)</span> )
 
;<br/>
<b>hence </b><a NAME="E3:29_1_1"/>
<font color="Maroon">z</font> <a href="quaterni.html#K7" target="_self">+</a> <font color="Maroon">z'</font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i>, , </i>;<br/>


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