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<div><span class="kw">theorem </span><a NAME="T19"><span class="comment"><font color="firebrick">:: QUATERN3:19</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">z1</font> being   <a href="quaterni.html#NM1" title="QUATERNI:NM.1">Quaternion</a> holds  <span class="p1">(<span class="default"><a href="quatern2.html#K3" title="QUATERN2:func.3">&lt;i&gt;</a> <a href="quaterni.html#K22" title="QUATERNI:func.22">*</a> <font color="Olive" title="b1">z1</font></span>)</span> <a href="quaterni.html#K21" title="QUATERNI:func.21">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">z1</font> <a href="quaterni.html#K22" title="QUATERNI:func.22">*</a> <a href="quatern2.html#K3" title="QUATERN2:func.3">&lt;i&gt;</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="quaterni.html#K5" title="QUATERNI:func.5">[*</a><span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p4">(<span class="default"><a href="quaterni.html#K13" title="QUATERNI:func.13">Im1</a> <font color="Olive" title="b1">z1</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><a href="quaterni.html#K12" title="QUATERNI:func.12">Rea</a> <font color="Olive" title="b1">z1</font></span>)</span></span>)</span>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="quaterni.html#K5" title="QUATERNI:func.5">*]</a></span></div></div>
