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<div class="add">

<b>let </b><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</font> be    <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/>



<b>assume </b><b>that </b><br/><a NAME="E1:85"/><i><font color="Green" title="E71">A1</font></i>: 
 <a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 <b>and </b><br/><a NAME="E2:85"/><i><font color="Green" title="E72">A2</font></i>: 
 <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 <b>and </b><br/><a NAME="E3:85"/><i><font color="Green" title="E73">A3</font></i>: 
0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a>  <a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c2">b</font>
 <b>and </b><br/><a NAME="E4:85"/><i><font color="Green" title="E74">A4</font></i>: 
 <a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c2">b</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a>  <a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a> 
 ;<br/>

<a NAME="E5:85"/>
<font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default">0 <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>
 
<b>by </b><i><a class="txt" href="complex2.html#E1:85"><i><font color="Green" title="E71">A1</font></i></a>, <a class="ref" href="complex1.html#T29" title="COMPLEX1:th.29">COMPLEX1:29</a></i>;<br/>
<a NAME="E6:85"/><b>then </b><i><font color="Green" title="E75">A5</font></i>: 
 <a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 
<b>by </b><i><a class="txt" href="complex2.html#E2:85"><i><font color="Green" title="E72">A2</font></i></a>, <a class="ref" href="comptrig.html#T53" title="COMPTRIG:th.53">COMPTRIG:53</a></i>;<br/>
<b>then </b><i><font color="Green" title="E76">A6</font></i>:  <a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p1">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <font color="Maroon" title="c1">a</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a> 
<b>by </b><i><a class="txt" href="complex2.html#E2:85"><i><font color="Green" title="E72">A2</font></i></a>, <a class="ref" href="complex2.html#T22" target="_self" title="COMPLEX2:th.22">Th22</a>, <a class="ref" href="complex1.html#T12" title="COMPLEX1:th.12">COMPLEX1:12</a>, <a class="ref" href="comptrig.html#T21" title="COMPTRIG:th.21">COMPTRIG:21</a></i>
<br/>.= 
 <a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a> 
<b>by </b><i><a class="txt" href="complex2.html#E6:85"><i><font color="Green" title="E75">A5</font></i></a></i>
;<br/>
<a NAME="E8:85"/>
 <a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c2">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">].</a><span class="default">0,<a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a> </span><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">.[</a></span>
 
<b>by </b><i><a class="txt" href="complex2.html#E3:85"><i><font color="Green" title="E73">A3</font></i></a>, <a class="txt" href="complex2.html#E4:85"><i><font color="Green" title="E74">A4</font></i></a>, <a class="ref" href="rcomp_1.html#T47" title="RCOMP_1:th.47">RCOMP_1:47</a></i>;<br/>
<a NAME="E9:85"/><b>then </b><i><font color="Green" title="E77">A7</font></i>: 
 <a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c2">b</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 
<b>by </b><i><a class="ref" href="complex2.html#T27" target="_self" title="COMPLEX2:th.27">Th27</a></i>;<br/>
<i><font color="Green" title="E78">A8</font></i>:  <a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c2">b</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c2">b</font></span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#T48" title="COMPLEX1:th.48">COMPLEX1:48</a></i>
<br/>.= 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c2">b</font></span>)</span>
<b>by </b><i><a class="txt" href="complex2.html#E1:85"><i><font color="Green" title="E71">A1</font></i></a></i>
;<br/>
<a NAME="E11:85"/>
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c2">b</font>
 
;<br/>
<a NAME="E12:85"/><b>then </b><i><font color="Green" title="E79">A9</font></i>: 
 <a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> 0
 
<b>by </b><i><a class="txt" href="complex2.html#E9:85"><i><font color="Green" title="E77">A7</font></i></a>, <a class="txt" href="complex2.html#E10:85"><i><font color="Green" title="E78">A8</font></i></a>, <a class="ref" href="xreal_1.html#T60" title="XREAL_1:th.60">XREAL_1:60</a></i>;<br/>
<a NAME="E13:85"/><b>then </b><i><font color="Green" title="E80">A10</font></i>: 
 <a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a> 
 
<b>by </b><i><a class="ref" href="complex2.html#T37" target="_self" title="COMPLEX2:th.37">Th37</a></i>;<br/>
<a NAME="E14:85"/>
<span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> </span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> </span>)</span></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0
 
<b>by </b><i><a class="txt" href="complex2.html#E3:85"><i><font color="Green" title="E73">A3</font></i></a>, <a class="txt" href="complex2.html#E6:85"><i><font color="Green" title="E75">A5</font></i></a></i>;<br/>
<a NAME="E15:85"/><b>then </b><i><font color="Green" title="E81">A11</font></i>: 
 <a href="complex2.html#K4" title="COMPLEX2:func.4">angle</a> <font color="Maroon" title="c1">a</font>,<a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> ,<font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c1">a</font></span>)</span>
 
<b>by </b><i><a class="ref" href="complex2.html#D6" target="_self" title="COMPLEX2:def.6">Def6</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="85_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font> be    <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/><b>assume </b><b>that </b><br/><a NAME="E1:85_3"/><i><font color="Green" title="E82">A12</font></i>: 
 <a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 <b>and </b><br/><a NAME="E2:85_3"/><i><font color="Green" title="E83">A13</font></i>: 
 <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c3">a</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 <b>and </b><br/><a NAME="E3:85_3"/><i><font color="Green" title="E84">A14</font></i>: 
0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a>  <a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font>
 <b>and </b><br/><a NAME="E4:85_3"/><i><font color="Green" title="E85">A15</font></i>: 
 <a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a>  <a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a> 
 ;<br/><a NAME="E5:85_3"/>
 <a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">].</a><span class="default">0,<a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a> </span><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">.[</a></span>
 <b>by </b><i><a class="txt" href="complex2.html#E3:85_3"><i><font color="Green" title="E84">A14</font></i></a>, <a class="txt" href="complex2.html#E4:85_3"><i><font color="Green" title="E85">A15</font></i></a>, <a class="ref" href="rcomp_1.html#T47" title="RCOMP_1:th.47">RCOMP_1:47</a></i>;<br/><a NAME="E6:85_3"/><b>then </b><i><font color="Green" title="E86">A16</font></i>: 
 <a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c4">b</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 <b>by </b><i><a class="ref" href="complex2.html#T27" target="_self" title="COMPLEX2:th.27">Th27</a></i>;<br/><i><font color="Green" title="E87">A17</font></i>:  <a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c3">a</font></span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#T48" title="COMPLEX1:th.48">COMPLEX1:48</a></i>
<br/>.= 
 <a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c4">b</font>
<b>by </b><i><a class="txt" href="complex2.html#E1:85_3"><i><font color="Green" title="E82">A12</font></i></a></i>
;<br/><a NAME="E8:85_3"/><i><font color="Green" title="E88">A18</font></i>: 
 <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c3">a</font></span>)</span>
 <b>by </b><i><a class="ref" href="complex1.html#T48" title="COMPLEX1:th.48">COMPLEX1:48</a></i>;<br/><a NAME="E9:85_3"/>
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c3">a</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c3">a</font>
 ;<br/><a NAME="E10:85_3"/><b>then </b>
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> 0
 <b>by </b><i><a class="txt" href="complex2.html#E2:85_3"><i><font color="Green" title="E83">A13</font></i></a>, <a class="ref" href="xreal_1.html#T60" title="XREAL_1:th.60">XREAL_1:60</a></i>;<br/><a NAME="E11:85_3"/><b>then </b><i><font color="Green" title="E89">A19</font></i>: 
<span class="p1">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c3">a</font></span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <span class="p1">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T10" title="XREAL_1:th.10">XREAL_1:10</a></i>;<br/><b>set </b><font color="Maroon" title="c5">ba</font> = <font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font>;<br/><b>set </b><font color="Maroon" title="c6">Rb</font> =  <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c4">b</font>;<br/><b>set </b><font color="Maroon" title="c7">Rba</font> =  <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span>;<br/><b>set </b><font color="Maroon" title="c8">Ib</font> =  <a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c4">b</font>;<br/><b>set </b><font color="Maroon" title="c9">Iba</font> =  <a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span>;<br/><b>set </b><font color="Maroon" title="c10">B</font> =  <a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font>;<br/><b>set </b><font color="Maroon" title="c11">BA</font> =  <a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span>;<br/><b>set </b><font color="Maroon" title="c12">mb</font> = <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><font color="Maroon" title="c4">b</font></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span>;<br/><b>set </b><font color="Maroon" title="c13">mba</font> = <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span>;<br/><a NAME="E12:85_3"/><i><font color="Green" title="E90">A20</font></i>: 
<font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><font color="Maroon" title="c4">b</font></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><font color="Maroon" title="c4">b</font></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span></span>)</span></span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span>
 <b>by </b><i><a class="ref" href="complex2.html#T19" target="_self" title="COMPLEX2:th.19">Th19</a></i>;<br/><font color="Maroon" title="c4">b</font> = 
<span class="p1">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c4">b</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"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c4">b</font></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>
<b>by </b><i><a class="ref" href="complex1.html#T29" title="COMPLEX1:th.29">COMPLEX1:29</a></i>
<br/>.= 
<span class="p1"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c4">b</font></span>)</span>,<span class="p2">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c4">b</font></span>)</span></span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span>
<b>by </b><i><a class="ref" href="complex1.html#T27" title="COMPLEX1:th.27">COMPLEX1:27</a></i>
;<br/><a NAME="E14:85_3"/><b>then </b><i><font color="Green" title="E91">A21</font></i>: 
(  <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><font color="Maroon" title="c4">b</font></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span> &amp;  <a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><font color="Maroon" title="c4">b</font></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span> )
 <b>by </b><i><a class="ref" href="arytm_0.html#T12" title="ARYTM_0:th.12">ARYTM_0:12</a>, <a class="txt" href="complex2.html#E12:85_3"><i><font color="Green" title="E90">A20</font></i></a></i>;<br/><a NAME="E15:85_3"/><i><font color="Green" title="E92">A22</font></i>: 
<font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span>
 <b>by </b><i><a class="ref" href="complex2.html#T19" target="_self" title="COMPLEX2:th.19">Th19</a></i>;<br/><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font> = 
<span class="p1">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></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"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></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>
<b>by </b><i><a class="ref" href="complex1.html#T29" title="COMPLEX1:th.29">COMPLEX1:29</a></i>
<br/>.= 
<span class="p1"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span>)</span></span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span>
<b>by </b><i><a class="ref" href="complex1.html#T27" title="COMPLEX1:th.27">COMPLEX1:27</a></i>
;<br/><a NAME="E17:85_3"/><b>then </b><i><font color="Green" title="E93">A23</font></i>: 
(  <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span>)</span></span>)</span> &amp;  <a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span>)</span></span>)</span> )
 <b>by </b><i><a class="ref" href="arytm_0.html#T12" title="ARYTM_0:th.12">ARYTM_0:12</a>, <a class="txt" href="complex2.html#E15:85_3"><i><font color="Green" title="E92">A22</font></i></a></i>;<br/><a NAME="E18:85_3"/><i><font color="Green" title="E94">A24</font></i>: 
<span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><font color="Maroon" title="c4">b</font></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="square_1.html#K7" title="SQUARE_1:func.7">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="complex1.html#D16" title="COMPLEX1:def.16">COMPLEX1:def 16</a></i>;<br/><a NAME="E19:85_3"/><i><font color="Green" title="E95">A25</font></i>: 
<span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="square_1.html#K7" title="SQUARE_1:func.7">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="complex2.html#E7:85_3"><i><font color="Green" title="E87">A17</font></i></a>, <a class="ref" href="complex1.html#D16" title="COMPLEX1:def.16">COMPLEX1:def 16</a></i>;<br/><a NAME="E20:85_3"/><i><font color="Green" title="E96">A26</font></i>: 
( <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><font color="Maroon" title="c4">b</font></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0 &amp; <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><font color="Maroon" title="c4">b</font></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0 )
 <b>by </b><i><a class="txt" href="complex2.html#E6:85_3"><i><font color="Green" title="E86">A16</font></i></a>, <a class="ref" href="complex1.html#T12" title="COMPLEX1:th.12">COMPLEX1:12</a>, <a class="ref" href="complex1.html#T133" title="COMPLEX1:th.133">COMPLEX1:133</a></i>;<br/><a NAME="E21:85_3"/><i><font color="Green" title="E97">A27</font></i>: 
( <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0 &amp; <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0 )
 <b>by </b><i><a class="txt" href="complex2.html#E6:85_3"><i><font color="Green" title="E86">A16</font></i></a>, <a class="txt" href="complex2.html#E7:85_3"><i><font color="Green" title="E87">A17</font></i></a>, <a class="ref" href="complex1.html#T12" title="COMPLEX1:th.12">COMPLEX1:12</a>, <a class="ref" href="complex1.html#T133" title="COMPLEX1:th.133">COMPLEX1:133</a></i>;<br/><a NAME="E22:85_3"/>
( <span class="p1">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a>  <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0 &amp; <span class="p1">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a>  <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0 )
 <b>by </b><i><a class="ref" href="xreal_1.html#T65" title="XREAL_1:th.65">XREAL_1:65</a></i>;<br/><a NAME="E23:85_3"/><b>then </b><i><font color="Green" title="E98">A28</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T9" title="XREAL_1:th.9">XREAL_1:9</a></i>;<br/><a NAME="E24:85_3"/>
( <span class="p1">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a>  <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0 &amp; <span class="p1">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a>  <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0 )
 <b>by </b><i><a class="ref" href="xreal_1.html#T65" title="XREAL_1:th.65">XREAL_1:65</a></i>;<br/><a NAME="E25:85_3"/><b>then </b><i><font color="Green" title="E99">A29</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T9" title="XREAL_1:th.9">XREAL_1:9</a></i>;<br/><a NAME="E26:85_3"/><i><font color="Green" title="E100">A30</font></i>: 
 <a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 <b>by </b><i><a class="txt" href="complex2.html#E6:85_3"><i><font color="Green" title="E86">A16</font></i></a>, <a class="txt" href="complex2.html#E7:85_3"><i><font color="Green" title="E87">A17</font></i></a>, <a class="ref" href="comptrig.html#T63" title="COMPTRIG:th.63">COMPTRIG:63</a></i>;<br/><a NAME="E27:85_3"/><b>then </b><i><font color="Green" title="E101">A31</font></i>: 
<span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><font color="Maroon" title="c4">b</font></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="complex2.html#E7:85_3"><i><font color="Green" title="E87">A17</font></i></a>, <a class="txt" href="complex2.html#E14:85_3"><i><font color="Green" title="E91">A21</font></i></a>, <a class="txt" href="complex2.html#E17:85_3"><i><font color="Green" title="E93">A23</font></i></a>, <a class="txt" href="complex2.html#E20:85_3"><i><font color="Green" title="E96">A26</font></i></a>, <a class="ref" href="xcmplx_1.html#T95" title="XCMPLX_1:th.95">XCMPLX_1:95</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="85_3_4"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:85_3_4"/>
( 0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a>  <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span> or 0 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span> or 0 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="85_3_4_1"><b>suppose </b></a><a NAME="E1:85_3_4_1"/><i><font color="Green" title="E102">A32</font></i>: 
0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a>  <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span>
 ;<br/><div class="add"><a NAME="E2:85_3_4_1"/><b>then </b><i><font color="Green" title="E103">A33</font></i>: 
 <a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">].</a><span class="default">0,<span class="p2">(<span class="default"><a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a>  <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2</span>)</span></span><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">.[</a></span>
 <b>by </b><i><a class="txt" href="complex2.html#E6:85_3"><i><font color="Green" title="E86">A16</font></i></a>, <a class="ref" href="comptrig.html#T59" title="COMPTRIG:th.59">COMPTRIG:59</a>, <a class="txt" href="complex2.html#E8:85_3"><i><font color="Green" title="E88">A18</font></i></a>, <a class="txt" href="complex2.html#E11:85_3"><i><font color="Green" title="E89">A19</font></i></a></i>;<br/><a NAME="E3:85_3_4_1"/><i><font color="Green" title="E104">A34</font></i>: 
 <a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">].</a><span class="default">0,<span class="p2">(<span class="default"><a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a>  <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2</span>)</span></span><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">.[</a></span>
 <b>by </b><i><a class="txt" href="complex2.html#E6:85_3"><i><font color="Green" title="E86">A16</font></i></a>, <a class="txt" href="complex2.html#E7:85_3"><i><font color="Green" title="E87">A17</font></i></a>, <a class="txt" href="complex2.html#E1:85_3_4_1"><i><font color="Green" title="E102">A32</font></i></a>, <a class="ref" href="comptrig.html#T59" title="COMPTRIG:th.59">COMPTRIG:59</a></i>;<br/><a NAME="E4:85_3_4_1"/>
<span class="p1">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a>  <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <span class="p1">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> 
 <b>by </b><i><a class="txt" href="complex2.html#E8:85_3"><i><font color="Green" title="E88">A18</font></i></a>, <a class="txt" href="complex2.html#E11:85_3"><i><font color="Green" title="E89">A19</font></i></a>, <a class="txt" href="complex2.html#E1:85_3_4_1"><i><font color="Green" title="E102">A32</font></i></a>, <a class="ref" href="square_1.html#T78" title="SQUARE_1:th.78">SQUARE_1:78</a></i>;<br/><a NAME="E5:85_3_4_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T10" title="XREAL_1:th.10">XREAL_1:10</a></i>;<br/><a NAME="E6:85_3_4_1"/><b>then </b>
<span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><font color="Maroon" title="c4">b</font></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span>
 <b>by </b><i><a class="txt" href="complex2.html#E18:85_3"><i><font color="Green" title="E94">A24</font></i></a>, <a class="txt" href="complex2.html#E19:85_3"><i><font color="Green" title="E95">A25</font></i></a>, <a class="txt" href="complex2.html#E23:85_3"><i><font color="Green" title="E98">A28</font></i></a>, <a class="ref" href="square_1.html#T95" title="SQUARE_1:th.95">SQUARE_1:95</a></i>;<br/><a NAME="E7:85_3_4_1"/><b>then </b>
<span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><font color="Maroon" title="c4">b</font></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> 1
 <b>by </b><i><a class="txt" href="complex2.html#E21:85_3"><i><font color="Green" title="E97">A27</font></i></a>, <a class="ref" href="real_2.html#T142" title="REAL_2:th.142">REAL_2:142</a></i>;<br/><a NAME="E8:85_3_4_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <span class="p3">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <span class="p3">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> 1 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="complex2.html#E26:85_3"><i><font color="Green" title="E100">A30</font></i></a>, <a class="txt" href="complex2.html#E27:85_3"><i><font color="Green" title="E101">A31</font></i></a>, <a class="ref" href="xreal_1.html#T70" title="XREAL_1:th.70">XREAL_1:70</a></i>;<br/><a NAME="E9:85_3_4_1"/><b>then </b>
 <a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> 1 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="complex2.html#E26:85_3"><i><font color="Green" title="E100">A30</font></i></a>, <a class="ref" href="xcmplx_1.html#T88" title="XCMPLX_1:th.88">XCMPLX_1:88</a></i>;<br/><a NAME="E10:85_3_4_1"/><b>then </b>
 <a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font>
 <b>by </b><i><a class="txt" href="complex2.html#E2:85_3_4_1"><i><font color="Green" title="E103">A33</font></i></a>, <a class="txt" href="complex2.html#E3:85_3_4_1"><i><font color="Green" title="E104">A34</font></i></a>, <a class="ref" href="complex2.html#T7" target="_self" title="COMPLEX2:th.7">Th7</a></i>;<br/><a NAME="E11:85_3_4_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T10" title="XREAL_1:th.10">XREAL_1:10</a></i>;<br/><b>hence </b><a NAME="E12:85_3_4_1"/>
<span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="85_3_4_2"><b>suppose </b></a><a NAME="E1:85_3_4_2"/><i><font color="Green" title="E102">A35</font></i>: 
0 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span>
 ;<br/><div class="add"><a NAME="E2:85_3_4_2"/><b>then </b>
<font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></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>
 <b>by </b><i><a class="ref" href="complex1.html#T29" title="COMPLEX1:th.29">COMPLEX1:29</a></i>;<br/><a NAME="E3:85_3_4_2"/><b>then </b><i><font color="Green" title="E103">A36</font></i>: 
 <a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a>  <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2
 <b>by </b><i><a class="txt" href="complex2.html#E6:85_3"><i><font color="Green" title="E86">A16</font></i></a>, <a class="txt" href="complex2.html#E7:85_3"><i><font color="Green" title="E87">A17</font></i></a>, <a class="ref" href="comptrig.html#T55" title="COMPTRIG:th.55">COMPTRIG:55</a></i>;<br/><a NAME="E4:85_3_4_2"/>
 <a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">].</a><span class="default">0,<span class="p2">(<span class="default"><a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a>  <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2</span>)</span></span><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">.[</a></span>
 <b>by </b><i><a class="txt" href="complex2.html#E6:85_3"><i><font color="Green" title="E86">A16</font></i></a>, <a class="txt" href="complex2.html#E8:85_3"><i><font color="Green" title="E88">A18</font></i></a>, <a class="txt" href="complex2.html#E11:85_3"><i><font color="Green" title="E89">A19</font></i></a>, <a class="txt" href="complex2.html#E1:85_3_4_2"><i><font color="Green" title="E102">A35</font></i></a>, <a class="ref" href="comptrig.html#T59" title="COMPTRIG:th.59">COMPTRIG:59</a></i>;<br/><a NAME="E5:85_3_4_2"/><b>then </b>
 <a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a>  <a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span>
 <b>by </b><i><a class="txt" href="complex2.html#E3:85_3_4_2"><i><font color="Green" title="E103">A36</font></i></a>, <a class="ref" href="rcomp_1.html#T47" title="RCOMP_1:th.47">RCOMP_1:47</a></i>;<br/><a NAME="E6:85_3_4_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T10" title="XREAL_1:th.10">XREAL_1:10</a></i>;<br/><b>hence </b><a NAME="E7:85_3_4_2"/>
<span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="85_3_4_3"><b>suppose </b></a><a NAME="E1:85_3_4_3"/><i><font color="Green" title="E102">A37</font></i>: 
0 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span>
 ;<br/><div class="add"><b>thus </b><a NAME="E2:85_3_4_3"/>
<span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="85_3_4_3_1"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="85_3_4_3_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:85_3_4_3_1_1"/>
( 0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a>  <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c4">b</font> or 0 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c4">b</font> or 0 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c4">b</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="85_3_4_3_1_1_1"><b>suppose </b></a><a NAME="E1:85_3_4_3_1_1_1"/>
0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a>  <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c4">b</font>
 ;<br/><div class="add"><a NAME="E2:85_3_4_3_1_1_1"/><b>then </b>
 <a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">].</a><span class="default">0,<span class="p2">(<span class="default"><a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a>  <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2</span>)</span></span><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">.[</a></span>
 <b>by </b><i><a class="txt" href="complex2.html#E6:85_3"><i><font color="Green" title="E86">A16</font></i></a>, <a class="ref" href="comptrig.html#T59" title="COMPTRIG:th.59">COMPTRIG:59</a></i>;<br/><a NAME="E3:85_3_4_3_1_1_1"/><b>then </b><i><font color="Green" title="E103">A38</font></i>: 
 <a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a>  <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2
 <b>by </b><i><a class="ref" href="rcomp_1.html#T47" title="RCOMP_1:th.47">RCOMP_1:47</a></i>;<br/><a NAME="E4:85_3_4_3_1_1_1"/>
 <a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">].</a><span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a>  <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2</span>)</span>,<a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a> </span><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">.[</a></span>
 <b>by </b><i><a class="txt" href="complex2.html#E6:85_3"><i><font color="Green" title="E86">A16</font></i></a>, <a class="txt" href="complex2.html#E7:85_3"><i><font color="Green" title="E87">A17</font></i></a>, <a class="txt" href="complex2.html#E1:85_3_4_3"><i><font color="Green" title="E102">A37</font></i></a>, <a class="ref" href="comptrig.html#T60" title="COMPTRIG:th.60">COMPTRIG:60</a></i>;<br/><a NAME="E5:85_3_4_3_1_1_1"/><b>then </b>
 <a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a>  <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2
 <b>by </b><i><a class="ref" href="rcomp_1.html#T47" title="RCOMP_1:th.47">RCOMP_1:47</a></i>;<br/><a NAME="E6:85_3_4_3_1_1_1"/><b>then </b>
 <a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font>
 <b>by </b><i><a class="txt" href="complex2.html#E3:85_3_4_3_1_1_1"><i><font color="Green" title="E103">A38</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E7:85_3_4_3_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T10" title="XREAL_1:th.10">XREAL_1:10</a></i>;<br/><b>hence </b><a NAME="E8:85_3_4_3_1_1_1"/>
<span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="85_3_4_3_1_1_2"><b>suppose </b></a><a NAME="E1:85_3_4_3_1_1_2"/>
0 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c4">b</font>
 ;<br/><div class="add"><a NAME="E2:85_3_4_3_1_1_2"/><b>then </b>
<font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c4">b</font></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>
 <b>by </b><i><a class="ref" href="complex1.html#T29" title="COMPLEX1:th.29">COMPLEX1:29</a></i>;<br/><a NAME="E3:85_3_4_3_1_1_2"/><b>then </b><i><font color="Green" title="E103">A39</font></i>: 
 <a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a>  <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2
 <b>by </b><i><a class="txt" href="complex2.html#E6:85_3"><i><font color="Green" title="E86">A16</font></i></a>, <a class="ref" href="comptrig.html#T55" title="COMPTRIG:th.55">COMPTRIG:55</a></i>;<br/><a NAME="E4:85_3_4_3_1_1_2"/>
 <a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">].</a><span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a>  <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2</span>)</span>,<a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a> </span><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">.[</a></span>
 <b>by </b><i><a class="txt" href="complex2.html#E6:85_3"><i><font color="Green" title="E86">A16</font></i></a>, <a class="txt" href="complex2.html#E7:85_3"><i><font color="Green" title="E87">A17</font></i></a>, <a class="txt" href="complex2.html#E1:85_3_4_3"><i><font color="Green" title="E102">A37</font></i></a>, <a class="ref" href="comptrig.html#T60" title="COMPTRIG:th.60">COMPTRIG:60</a></i>;<br/><a NAME="E5:85_3_4_3_1_1_2"/><b>then </b>
 <a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a>  <a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span>
 <b>by </b><i><a class="txt" href="complex2.html#E3:85_3_4_3_1_1_2"><i><font color="Green" title="E103">A39</font></i></a>, <a class="ref" href="rcomp_1.html#T47" title="RCOMP_1:th.47">RCOMP_1:47</a></i>;<br/><a NAME="E6:85_3_4_3_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T10" title="XREAL_1:th.10">XREAL_1:10</a></i>;<br/><b>hence </b><a NAME="E7:85_3_4_3_1_1_2"/>
<span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="85_3_4_3_1_1_3"><b>suppose </b></a><a NAME="E1:85_3_4_3_1_1_3"/><i><font color="Green" title="E103">A40</font></i>: 
0 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c4">b</font>
 ;<br/><div class="add"><a NAME="E2:85_3_4_3_1_1_3"/><b>then </b><i><font color="Green" title="E104">A41</font></i>: 
 <a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">].</a><span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a>  <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2</span>)</span>,<a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a> </span><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">.[</a></span>
 <b>by </b><i><a class="txt" href="complex2.html#E6:85_3"><i><font color="Green" title="E86">A16</font></i></a>, <a class="ref" href="comptrig.html#T60" title="COMPTRIG:th.60">COMPTRIG:60</a></i>;<br/><a NAME="E3:85_3_4_3_1_1_3"/><i><font color="Green" title="E105">A42</font></i>: 
 <a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">].</a><span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a>  <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2</span>)</span>,<a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a> </span><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">.[</a></span>
 <b>by </b><i><a class="txt" href="complex2.html#E6:85_3"><i><font color="Green" title="E86">A16</font></i></a>, <a class="txt" href="complex2.html#E7:85_3"><i><font color="Green" title="E87">A17</font></i></a>, <a class="txt" href="complex2.html#E1:85_3_4_3"><i><font color="Green" title="E102">A37</font></i></a>, <a class="ref" href="comptrig.html#T60" title="COMPTRIG:th.60">COMPTRIG:60</a></i>;<br/><a NAME="E4:85_3_4_3_1_1_3"/>
<span class="p1">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <span class="p1">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> 
 <b>by </b><i><a class="txt" href="complex2.html#E8:85_3"><i><font color="Green" title="E88">A18</font></i></a>, <a class="txt" href="complex2.html#E11:85_3"><i><font color="Green" title="E89">A19</font></i></a>, <a class="txt" href="complex2.html#E1:85_3_4_3_1_1_3"><i><font color="Green" title="E103">A40</font></i></a>, <a class="ref" href="square_1.html#T114" title="SQUARE_1:th.114">SQUARE_1:114</a></i>;<br/><a NAME="E5:85_3_4_3_1_1_3"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T10" title="XREAL_1:th.10">XREAL_1:10</a></i>;<br/><a NAME="E6:85_3_4_3_1_1_3"/><b>then </b>
<span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><font color="Maroon" title="c4">b</font></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span>
 <b>by </b><i><a class="txt" href="complex2.html#E18:85_3"><i><font color="Green" title="E94">A24</font></i></a>, <a class="txt" href="complex2.html#E19:85_3"><i><font color="Green" title="E95">A25</font></i></a>, <a class="txt" href="complex2.html#E25:85_3"><i><font color="Green" title="E99">A29</font></i></a>, <a class="ref" href="square_1.html#T95" title="SQUARE_1:th.95">SQUARE_1:95</a></i>;<br/><a NAME="E7:85_3_4_3_1_1_3"/><b>then </b>
<span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><font color="Maroon" title="c4">b</font></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 <b>by </b><i><a class="txt" href="complex2.html#E20:85_3"><i><font color="Green" title="E96">A26</font></i></a>, <a class="ref" href="real_2.html#T142" title="REAL_2:th.142">REAL_2:142</a></i>;<br/><a NAME="E8:85_3_4_3_1_1_3"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <span class="p3">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <span class="p3">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="complex2.html#E26:85_3"><i><font color="Green" title="E100">A30</font></i></a>, <a class="txt" href="complex2.html#E27:85_3"><i><font color="Green" title="E101">A31</font></i></a>, <a class="ref" href="xreal_1.html#T70" title="XREAL_1:th.70">XREAL_1:70</a></i>;<br/><a NAME="E9:85_3_4_3_1_1_3"/><b>then </b>
 <a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="complex2.html#E26:85_3"><i><font color="Green" title="E100">A30</font></i></a>, <a class="ref" href="xcmplx_1.html#T88" title="XCMPLX_1:th.88">XCMPLX_1:88</a></i>;<br/><a NAME="E10:85_3_4_3_1_1_3"/><b>then </b>
 <a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font>
 <b>by </b><i><a class="txt" href="complex2.html#E2:85_3_4_3_1_1_3"><i><font color="Green" title="E104">A41</font></i></a>, <a class="txt" href="complex2.html#E3:85_3_4_3_1_1_3"><i><font color="Green" title="E105">A42</font></i></a>, <a class="ref" href="complex2.html#T8" target="_self" title="COMPLEX2:th.8">Th8</a></i>;<br/><a NAME="E11:85_3_4_3_1_1_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T10" title="XREAL_1:th.10">XREAL_1:10</a></i>;<br/><b>hence </b><a NAME="E12:85_3_4_3_1_1_3"/>
<span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c3">a</font></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<a NAME="E17:85"/><b>then </b>
<span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c1">a</font></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 
<b>by </b><i><a class="txt" href="complex2.html#E1:85"><i><font color="Green" title="E71">A1</font></i></a>, <a class="txt" href="complex2.html#E2:85"><i><font color="Green" title="E72">A2</font></i></a>, <a class="txt" href="complex2.html#E3:85"><i><font color="Green" title="E73">A3</font></i></a>, <a class="txt" href="complex2.html#E4:85"><i><font color="Green" title="E74">A4</font></i></a></i>;<br/>
<a NAME="E18:85"/><b>then </b>
<span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p2">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 
;<br/>
<a NAME="E19:85"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a> </span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 
<b>by </b><i><a class="txt" href="complex2.html#E12:85"><i><font color="Green" title="E79">A9</font></i></a>, <a class="txt" href="complex2.html#E13:85"><i><font color="Green" title="E80">A10</font></i></a>, <a class="ref" href="complex2.html#T22" target="_self" title="COMPLEX2:th.22">Th22</a>, <a class="ref" href="complex1.html#T12" title="COMPLEX1:th.12">COMPLEX1:12</a></i>;<br/>
<a NAME="E20:85"/><b>then </b>
<span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a> </span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 
;<br/>
<a NAME="E21:85"/><b>then </b><i><font color="Green" title="E82">A43</font></i>: 
<span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p2">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 
<b>by </b><i><a class="txt" href="complex2.html#E4:85"><i><font color="Green" title="E74">A4</font></i></a>, <a class="txt" href="complex2.html#E9:85"><i><font color="Green" title="E77">A7</font></i></a>, <a class="ref" href="complex2.html#T22" target="_self" title="COMPLEX2:th.22">Th22</a>, <a class="ref" href="complex1.html#T12" title="COMPLEX1:th.12">COMPLEX1:12</a></i>;<br/>
<a NAME="E22:85"/><b>then </b><i><font color="Green" title="E83">A44</font></i>: 
<span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p2">(<span class="default"><a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a>  <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 
;<br/>
<a NAME="E23:85"/><i><font color="Green" title="E84">A45</font></i>: 
 <a href="complex2.html#K4" title="COMPLEX2:func.4">angle</a> <a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> ,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p2">(<span class="default"><a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a>  <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="complex2.html#E21:85"><i><font color="Green" title="E82">A43</font></i></a>, <a class="ref" href="complex2.html#D6" target="_self" title="COMPLEX2:def.6">Def6</a></i>;<br/>
<a NAME="E24:85"/>
 <a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a> 
 
<b>by </b><i><a class="txt" href="complex2.html#E12:85"><i><font color="Green" title="E79">A9</font></i></a>, <a class="txt" href="complex2.html#E13:85"><i><font color="Green" title="E80">A10</font></i></a>, <a class="ref" href="complex2.html#T26" target="_self" title="COMPLEX2:th.26">Th26</a>, <a class="ref" href="complex1.html#T12" title="COMPLEX1:th.12">COMPLEX1:12</a></i>;<br/>
<a NAME="E25:85"/><b>then </b>
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c1">a</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a> 
 
<b>by </b><i><a class="ref" href="xreal_1.html#T26" title="XREAL_1:th.26">XREAL_1:26</a></i>;<br/>
<a NAME="E26:85"/><b>then </b>
<span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p2">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <font color="Maroon" title="c1">a</font></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c1">a</font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default">0 <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a> </span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a> 
 
<b>by </b><i><a class="txt" href="complex2.html#E7:85"><i><font color="Green" title="E76">A6</font></i></a>, <a class="ref" href="xreal_1.html#T9" title="XREAL_1:th.9">XREAL_1:9</a></i>;<br/>
<a NAME="E27:85"/><b>then </b><i><font color="Green" title="E85">A46</font></i>: 
 <a href="complex2.html#K4" title="COMPLEX2:func.4">angle</a> <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">a</font>,<a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p2">(<span class="default"><a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a>  <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c1">a</font></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c1">a</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="complex2.html#D6" target="_self" title="COMPLEX2:def.6">Def6</a></i>;<br/>
<i><font color="Green" title="E86">A47</font></i>: <span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p2">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a> </span>)</span>
<b>by </b><i><a class="txt" href="complex2.html#E4:85"><i><font color="Green" title="E74">A4</font></i></a>, <a class="txt" href="complex2.html#E9:85"><i><font color="Green" title="E77">A7</font></i></a>, <a class="ref" href="complex2.html#T22" target="_self" title="COMPLEX2:th.22">Th22</a>, <a class="ref" href="complex1.html#T12" title="COMPLEX1:th.12">COMPLEX1:12</a></i>
<br/>.= 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a> 

;<br/>
<i><font color="Green" title="E87">A48</font></i>: <span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p2">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <font color="Maroon" title="c1">a</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a> </span>)</span>
<b>by </b><i><a class="txt" href="complex2.html#E2:85"><i><font color="Green" title="E72">A2</font></i></a>, <a class="txt" href="complex2.html#E6:85"><i><font color="Green" title="E75">A5</font></i></a>, <a class="ref" href="complex2.html#T22" target="_self" title="COMPLEX2:th.22">Th22</a>, <a class="ref" href="complex1.html#T12" title="COMPLEX1:th.12">COMPLEX1:12</a>, <a class="ref" href="comptrig.html#T21" title="COMPTRIG:th.21">COMPTRIG:21</a></i>
<br/>.= 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a> 

;<br/>
<i><font color="Green" title="E88">A49</font></i>: <span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c1">a</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p2">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a> </span>)</span>
<b>by </b><i><a class="txt" href="complex2.html#E12:85"><i><font color="Green" title="E79">A9</font></i></a>, <a class="txt" href="complex2.html#E13:85"><i><font color="Green" title="E80">A10</font></i></a>, <a class="ref" href="complex2.html#T22" target="_self" title="COMPLEX2:th.22">Th22</a>, <a class="ref" href="complex1.html#T12" title="COMPLEX1:th.12">COMPLEX1:12</a></i>
<br/>.= 
 <a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a> 

;<br/>
<b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex2.html#K4" title="COMPLEX2:func.4">angle</a> <font color="Maroon" title="c1">a</font>,<a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> ,<font color="Maroon" title="c2">b</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="complex2.html#K4" title="COMPLEX2:func.4">angle</a> <a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> ,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="complex2.html#K4" title="COMPLEX2:func.4">angle</a> <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">a</font>,<a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> </span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p4">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p5">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p3">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c1">a</font></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p3">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <font color="Maroon" title="c1">a</font></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c1">a</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="complex2.html#E15:85"><i><font color="Green" title="E81">A11</font></i></a>, <a class="txt" href="complex2.html#E23:85"><i><font color="Green" title="E84">A45</font></i></a>, <a class="txt" href="complex2.html#E27:85"><i><font color="Green" title="E85">A46</font></i></a></i>
<br/>.= 
 <a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a> 
<b>by </b><i><a class="txt" href="complex2.html#E30:85"><i><font color="Green" title="E88">A49</font></i></a>, <a class="txt" href="complex2.html#E28:85"><i><font color="Green" title="E86">A47</font></i></a>, <a class="txt" href="complex2.html#E29:85"><i><font color="Green" title="E87">A48</font></i></a></i>
;<br/>

<b>thus </b><a NAME="E32:85"/>
0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a>  <a href="complex2.html#K4" title="COMPLEX2:func.4">angle</a> <a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> ,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">a</font>
 <b>by </b><i><a class="txt" href="complex2.html#E22:85"><i><font color="Green" title="E83">A44</font></i></a>, <a class="ref" href="complex2.html#D6" target="_self" title="COMPLEX2:def.6">Def6</a></i>;<br/>

<a NAME="E33:85"/><i><font color="Green" title="E89">A50</font></i>: 
<span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p2">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <font color="Maroon" title="c1">a</font></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a> </span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="complex2.html#E29:85"><i><font color="Green" title="E87">A48</font></i></a></i>;<br/>
<a NAME="E34:85"/>
2 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a>  <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="comptrig.html#T52" title="COMPTRIG:th.52">COMPTRIG:52</a></i>;<br/>
<a NAME="E35:85"/><b>then </b>
( <span class="p1">(<span class="default">2 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a> </span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0 &amp;  <a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0 )
 
<b>by </b><i><a class="ref" href="comptrig.html#T52" title="COMPTRIG:th.52">COMPTRIG:52</a>, <a class="ref" href="xreal_1.html#T22" title="XREAL_1:th.22">XREAL_1:22</a></i>;<br/>
<a NAME="E36:85"/><b>then </b>
<span class="p1">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a> </span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p2">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 0
 
<b>by </b><i><a class="ref" href="xreal_1.html#T10" title="XREAL_1:th.10">XREAL_1:10</a></i>;<br/>
<b>hence </b><a NAME="E37:85"/>
0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a>  <a href="complex2.html#K4" title="COMPLEX2:func.4">angle</a> <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">a</font>,<a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> 
 <b>by </b><i><a class="txt" href="complex2.html#E27:85"><i><font color="Green" title="E85">A46</font></i></a>, <a class="txt" href="complex2.html#E30:85"><i><font color="Green" title="E88">A49</font></i></a>, <a class="txt" href="complex2.html#E33:85"><i><font color="Green" title="E89">A50</font></i></a></i>;<br/>


</div>
