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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E14">Th34</font></span>: <a NAME="T34"><span class="comment"><font color="firebrick">:: POLYEQ_3:34</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">z</font> being   <a href="xcmplx_0.html#NM1" title="XCMPLX_0:NM.1">Complex</a><br/>  for <font color="Olive" title="b2">n</font>, <font color="Olive" title="b3">k</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st <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="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b2">n</font> <a href="power.html#K1" title="POWER:func.1">-root</a> <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></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#K19" title="SIN_COS:func.19">cos</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Olive" title="b1">z</font></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">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <a href="sin_cos.html#K28" title="SIN_COS:func.28">PI</a></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b3">k</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Olive" title="b2">n</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive" title="b2">n</font> <a href="power.html#K1" title="POWER:func.1">-root</a> <span class="p5"><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></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K17" title="SIN_COS:func.17">sin</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Olive" title="b1">z</font></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">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <a href="sin_cos.html#K28" title="SIN_COS:func.28">PI</a></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b3">k</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Olive" title="b2">n</font></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></span>)</span> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Olive" title="b2">n</font></div></div>
