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<div><span class="kw">theorem </span><a NAME="T54"><span class="comment"><font color="firebrick">:: COMPTRIG:54</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">z</font> being    <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/>  for <font color="Olive" title="b2">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st ( <font color="Olive" title="b1">z</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  or <font color="Olive" title="b2">n</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  ) holds <br/><font color="Olive" title="b1">z</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Olive" title="b2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K9" title="COMPLEX1:func.9">|.</a><span class="default"><font color="Olive" title="b1">z</font></span><a href="complex1.html#K9" title="COMPLEX1:func.9">.|</a></span> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Olive" title="b2">n</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="sin_cos.html#K19" title="SIN_COS:func.19">cos</a> <span class="p3">(<span class="default"><font color="Olive" title="b2">n</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Olive" title="b1">z</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="complex1.html#K9" title="COMPLEX1:func.9">|.</a><span class="default"><font color="Olive" title="b1">z</font></span><a href="complex1.html#K9" title="COMPLEX1:func.9">.|</a></span> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Olive" title="b2">n</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K17" title="SIN_COS:func.17">sin</a> <span class="p4">(<span class="default"><font color="Olive" title="b2">n</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p5">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Olive" title="b1">z</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a></span>)</span></div></div>
