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<div><span class="kw">theorem </span><a NAME="T74"><span class="comment"><font color="firebrick">:: QUATERN3:74</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">z1</font>, <font color="Olive" title="b2">z2</font> being   <a href="quaterni.html#NM1" title="QUATERNI:NM.1">Quaternion</a> holds  <font color="Olive" title="b1">z1</font> <a href="quatern2.html#K5" title="QUATERN2:func.5">/</a> <font color="Olive" title="b2">z2</font> <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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="quaterni.html#K12" title="QUATERNI:func.12">Rea</a> <font color="Olive" title="b2">z2</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<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="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="quaterni.html#K13" title="QUATERNI:func.13">Im1</a> <font color="Olive" title="b1">z1</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="quaterni.html#K13" title="QUATERNI:func.13">Im1</a> <font color="Olive" title="b2">z2</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="quaterni.html#K14" title="QUATERNI:func.14">Im2</a> <font color="Olive" title="b2">z2</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p0">(<span class="default"><a href="quaterni.html#K14" title="QUATERNI:func.14">Im2</a> <font color="Olive" title="b1">z1</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="quaterni.html#K15" title="QUATERNI:func.15">Im3</a> <font color="Olive" title="b2">z2</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p5">(<span class="default"><a href="quaterni.html#K15" title="QUATERNI:func.15">Im3</a> <font color="Olive" title="b1">z1</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default"><span class="p4"><a href="quaterni.html#K27" title="QUATERNI:func.27">|.</a><span class="default"><font color="Olive" title="b2">z2</font></span><a href="quaterni.html#K27" title="QUATERNI:func.27">.|</a></span> <a href="square_1.html#K1" title="SQUARE_1:func.1">^2</a></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="quaterni.html#K12" title="QUATERNI:func.12">Rea</a> <font color="Olive" title="b2">z2</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<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> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="quaterni.html#K13" title="QUATERNI:func.13">Im1</a> <font color="Olive" title="b2">z2</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<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></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="quaterni.html#K14" title="QUATERNI:func.14">Im2</a> <font color="Olive" title="b2">z2</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p0">(<span class="default"><a href="quaterni.html#K15" title="QUATERNI:func.15">Im3</a> <font color="Olive" title="b1">z1</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="quaterni.html#K15" title="QUATERNI:func.15">Im3</a> <font color="Olive" title="b2">z2</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p5">(<span class="default"><a href="quaterni.html#K14" title="QUATERNI:func.14">Im2</a> <font color="Olive" title="b1">z1</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default"><span class="p4"><a href="quaterni.html#K27" title="QUATERNI:func.27">|.</a><span class="default"><font color="Olive" title="b2">z2</font></span><a href="quaterni.html#K27" title="QUATERNI:func.27">.|</a></span> <a href="square_1.html#K1" title="SQUARE_1:func.1">^2</a></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="quaterni.html#K12" title="QUATERNI:func.12">Rea</a> <font color="Olive" title="b2">z2</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="quaterni.html#K14" title="QUATERNI:func.14">Im2</a> <font color="Olive" title="b1">z1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="quaterni.html#K13" title="QUATERNI:func.13">Im1</a> <font color="Olive" title="b2">z2</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="quaterni.html#K15" title="QUATERNI:func.15">Im3</a> <font color="Olive" title="b1">z1</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="quaterni.html#K14" title="QUATERNI:func.14">Im2</a> <font color="Olive" title="b2">z2</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p0">(<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></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="quaterni.html#K15" title="QUATERNI:func.15">Im3</a> <font color="Olive" title="b2">z2</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p5">(<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> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default"><span class="p4"><a href="quaterni.html#K27" title="QUATERNI:func.27">|.</a><span class="default"><font color="Olive" title="b2">z2</font></span><a href="quaterni.html#K27" title="QUATERNI:func.27">.|</a></span> <a href="square_1.html#K1" title="SQUARE_1:func.1">^2</a></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="quaterni.html#K12" title="QUATERNI:func.12">Rea</a> <font color="Olive" title="b2">z2</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="quaterni.html#K15" title="QUATERNI:func.15">Im3</a> <font color="Olive" title="b1">z1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="quaterni.html#K13" title="QUATERNI:func.13">Im1</a> <font color="Olive" title="b2">z2</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="quaterni.html#K14" title="QUATERNI:func.14">Im2</a> <font color="Olive" title="b1">z1</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="quaterni.html#K14" title="QUATERNI:func.14">Im2</a> <font color="Olive" title="b2">z2</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p0">(<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> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="quaterni.html#K15" title="QUATERNI:func.15">Im3</a> <font color="Olive" title="b2">z2</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p5">(<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></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default"><span class="p4"><a href="quaterni.html#K27" title="QUATERNI:func.27">|.</a><span class="default"><font color="Olive" title="b2">z2</font></span><a href="quaterni.html#K27" title="QUATERNI:func.27">.|</a></span> <a href="square_1.html#K1" title="SQUARE_1:func.1">^2</a></span>)</span></span>)</span></span><a href="quaterni.html#K5" title="QUATERNI:func.5">*]</a></span></div></div>
