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<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="E1:88"/><i><font color="Green" title="E74">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>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>and </b><br/><a NAME="E2:88"/><i><font color="Green" title="E75">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>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>and </b><br/><a NAME="E3:88"/><i><font color="Green" title="E76">A3</font></i>: 
 <a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <font color="Maroon" title="c2">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> 
 ;<br/>

<a NAME="E4:88"/>
<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"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <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#E1:88"><i><font color="Green" title="E74">A1</font></i></a>, <a class="ref" href="complex1.html#T29" title="COMPLEX1:th.29">COMPLEX1:29</a></i>;<br/>
<a NAME="E5:88"/><b>then </b><i><font color="Green" title="E77">A4</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>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="txt" href="complex2.html#E2:88"><i><font color="Green" title="E75">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="E78">A5</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#K7" title="REAL_1:func.7">+</a> <a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a> 
<b>by </b><i><a class="txt" href="complex2.html#E2:88"><i><font color="Green" title="E75">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#E5:88"><i><font color="Green" title="E77">A4</font></i></a></i>
;<br/>
<a NAME="E7:88"/><i><font color="Green" title="E79">A6</font></i>: 
(  <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c2">b</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp;  <a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 
<b>by </b><i><a class="txt" href="complex2.html#E3:88"><i><font color="Green" title="E76">A3</font></i></a>, <a class="ref" href="complex2.html#T35" target="_self" title="COMPLEX2:th.35">Th35</a></i>;<br/>
<i><font color="Green" title="E80">A7</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#K9" title="REAL_1:func.9">-</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#E1:88"><i><font color="Green" title="E74">A1</font></i></a></i>
;<br/>
<a NAME="E9:88"/><i><font color="Green" title="E81">A8</font></i>: 
<span class="p1">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <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="c1">a</font>
 
<b>by </b><i><a class="txt" href="complex2.html#E2:88"><i><font color="Green" title="E75">A2</font></i></a>, <a class="txt" href="complex2.html#E3:88"><i><font color="Green" title="E76">A3</font></i></a>, <a class="ref" href="complex2.html#T35" target="_self" title="COMPLEX2:th.35">Th35</a></i>;<br/>
<a NAME="E10:88"/><b>then </b>
<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="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</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="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="ref" href="xreal_1.html#T22" title="XREAL_1:th.22">XREAL_1:22</a></i>;<br/>
<a NAME="E11:88"/><b>then </b><i><font color="Green" title="E82">A9</font></i>: 
 <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</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="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="ref" href="complex1.html#T48" title="COMPLEX1:th.48">COMPLEX1:48</a></i>;<br/>
<a NAME="E12:88"/><b>then </b><i><font color="Green" title="E83">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="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="txt" href="complex2.html#E7:88"><i><font color="Green" title="E79">A6</font></i></a>, <a class="txt" href="complex2.html#E8:88"><i><font color="Green" title="E80">A7</font></i></a>, <a class="ref" href="complex2.html#T34" target="_self" title="COMPLEX2:th.34">Th34</a></i>;<br/>
<a NAME="E13:88"/>
 <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"><span class="p3">(<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="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</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>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="txt" href="complex2.html#E9:88"><i><font color="Green" title="E81">A8</font></i></a>, <a class="ref" href="xreal_1.html#T22" title="XREAL_1:th.22">XREAL_1:22</a></i>;<br/>
<a NAME="E14:88"/><b>then </b>
<span class="p1">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</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="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="ref" href="xreal_1.html#T60" title="XREAL_1:th.60">XREAL_1:60</a></i>;<br/>
<a NAME="E15:88"/><b>then </b><i><font color="Green" title="E84">A11</font></i>: 
 <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</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="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="ref" href="complex1.html#T48" title="COMPLEX1:th.48">COMPLEX1:48</a></i>;<br/>
<i><font color="Green" title="E85">A12</font></i>:  <a href="complex1.html#K4" title="COMPLEX1:func.4">Im</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> = 
<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> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <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>
<b>by </b><i><a class="ref" href="complex1.html#T48" title="COMPLEX1:th.48">COMPLEX1:48</a></i>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<b>by </b><i><a class="txt" href="complex2.html#E1:88"><i><font color="Green" title="E74">A1</font></i></a>, <a class="txt" href="complex2.html#E3:88"><i><font color="Green" title="E76">A3</font></i></a>, <a class="ref" href="complex2.html#T35" target="_self" title="COMPLEX2:th.35">Th35</a></i>
;<br/>
<a NAME="E17:88"/><b>then </b><i><font color="Green" title="E86">A13</font></i>: 
 <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="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a> 
 
<b>by </b><i><a class="txt" href="complex2.html#E15:88"><i><font color="Green" title="E84">A11</font></i></a>, <a class="ref" href="complex2.html#T35" target="_self" title="COMPLEX2:th.35">Th35</a></i>;<br/>
<a NAME="E18:88"/><i><font color="Green" title="E87">A14</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="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#K9" title="REAL_1:func.9">-</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#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="txt" href="complex2.html#E3:88"><i><font color="Green" title="E76">A3</font></i></a>, <a class="txt" href="complex2.html#E5:88"><i><font color="Green" title="E77">A4</font></i></a>, <a class="ref" href="comptrig.html#T21" title="COMPTRIG:th.21">COMPTRIG:21</a></i>;<br/>
<a NAME="E19:88"/><b>then </b><i><font color="Green" title="E88">A15</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#K9" title="REAL_1:func.9">-</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/>
<a NAME="E20:88"/><i><font color="Green" title="E89">A16</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="c2">b</font></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="c2">b</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a> 
 
<b>by </b><i><a class="txt" href="complex2.html#E3:88"><i><font color="Green" title="E76">A3</font></i></a>, <a class="txt" href="complex2.html#E21"><i><font color="Green" title="E13">Lm2</font></i></a>, <a class="ref" href="complex2.html#T22" target="_self" title="COMPLEX2:th.22">Th22</a>, <a class="ref" href="comptrig.html#T21" title="COMPTRIG:th.21">COMPTRIG:21</a></i>;<br/>
<a NAME="E21:88"/><i><font color="Green" title="E90">A17</font></i>: 
<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#K7" title="REAL_1:func.7">+</a> <a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</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="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="txt" href="complex2.html#E3:88"><i><font color="Green" title="E76">A3</font></i></a>, <a class="txt" href="complex2.html#E7:88"><i><font color="Green" title="E79">A6</font></i></a>, <a class="txt" href="complex2.html#E8:88"><i><font color="Green" title="E80">A7</font></i></a>, <a class="txt" href="complex2.html#E11:88"><i><font color="Green" title="E82">A9</font></i></a>, <a class="ref" href="complex2.html#T34" target="_self" title="COMPLEX2:th.34">Th34</a></i>;<br/>
<a NAME="E22:88"/><i><font color="Green" title="E91">A18</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#K9" title="REAL_1:func.9">-</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="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="txt" href="complex2.html#E3:88"><i><font color="Green" title="E76">A3</font></i></a>, <a class="txt" href="complex2.html#E7:88"><i><font color="Green" title="E79">A6</font></i></a>, <a class="txt" href="complex2.html#E8:88"><i><font color="Green" title="E80">A7</font></i></a>, <a class="txt" href="complex2.html#E11:88"><i><font color="Green" title="E82">A9</font></i></a>, <a class="txt" href="complex2.html#E20:88"><i><font color="Green" title="E89">A16</font></i></a>, <a class="ref" href="complex2.html#T34" target="_self" title="COMPLEX2:th.34">Th34</a></i>;<br/>
<a NAME="E23:88"/><i><font color="Green" title="E92">A19</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#K9" title="REAL_1:func.9">-</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#E20:88"><i><font color="Green" title="E89">A16</font></i></a>, <a class="txt" href="complex2.html#E21:88"><i><font color="Green" title="E90">A17</font></i></a>, <a class="ref" href="complex2.html#D6" target="_self" title="COMPLEX2:def.6">Def6</a></i>;<br/>
<a NAME="E24:88"/><i><font color="Green" title="E93">A20</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#K9" title="REAL_1:func.9">-</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>
 
<b>by </b><i><a class="txt" href="complex2.html#E22:88"><i><font color="Green" title="E91">A18</font></i></a>, <a class="ref" href="complex2.html#D6" target="_self" title="COMPLEX2:def.6">Def6</a></i>;<br/>
<a NAME="E25:88"/>
 <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="hidden.html#R1" title="HIDDEN:pred.1">=</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="txt" href="complex2.html#E15:88"><i><font color="Green" title="E84">A11</font></i></a>, <a class="txt" href="complex2.html#E16:88"><i><font color="Green" title="E85">A12</font></i></a>, <a class="ref" href="complex2.html#T35" target="_self" title="COMPLEX2:th.35">Th35</a></i>;<br/>
<a NAME="E26:88"/><b>then </b><i><font color="Green" title="E94">A21</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#K9" title="REAL_1:func.9">-</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="txt" href="complex2.html#E6:88"><i><font color="Green" title="E78">A5</font></i></a>, <a class="ref" href="complex2.html#D6" target="_self" title="COMPLEX2:def.6">Def6</a></i>;<br/>
<a NAME="E27:88"/><i><font color="Green" title="E95">A22</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="c2">b</font></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="c2">b</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a> 
 
<b>by </b><i><a class="txt" href="complex2.html#E3:88"><i><font color="Green" title="E76">A3</font></i></a>, <a class="txt" href="complex2.html#E21"><i><font color="Green" title="E13">Lm2</font></i></a>, <a class="ref" href="complex2.html#T22" target="_self" title="COMPLEX2:th.22">Th22</a>, <a class="ref" href="comptrig.html#T21" title="COMPTRIG:th.21">COMPTRIG:21</a></i>;<br/>
<i><font color="Green" title="E96">A23</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#K9" title="REAL_1:func.9">-</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#K9" title="REAL_1:func.9">-</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#K7" title="REAL_1:func.7">+</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#E2:88"><i><font color="Green" title="E75">A2</font></i></a>, <a class="txt" href="complex2.html#E5:88"><i><font color="Green" title="E77">A4</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/>
<b>thus </b><i><font color="Green" title="E97">A24</font></i>: <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="numbers.html#K6" title="NUMBERS:func.6">0</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="numbers.html#K6" title="NUMBERS:func.6">0</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="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<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#K9" title="REAL_1:func.9">-</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#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><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="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#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><a href="comptrig.html#K1" title="COMPTRIG:func.1">Arg</a> <span class="p4">(<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></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</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="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</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#E18:88"><i><font color="Green" title="E87">A14</font></i></a>, <a class="txt" href="complex2.html#E24:88"><i><font color="Green" title="E93">A20</font></i></a>, <a class="txt" href="complex2.html#E26:88"><i><font color="Green" title="E94">A21</font></i></a>, <a class="ref" href="complex2.html#D6" target="_self" title="COMPLEX2:def.6">Def6</a></i>
<br/>.= 
<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#K9" title="REAL_1:func.9">-</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#K9" title="REAL_1:func.9">-</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#K7" title="REAL_1:func.7">+</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#K7" title="REAL_1:func.7">+</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#K9" title="REAL_1:func.9">-</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>

<br/>.= 
 <a href="sin_cos.html#K35" title="SIN_COS:func.35">PI</a> 
<b>by </b><i><a class="txt" href="complex2.html#E12:88"><i><font color="Green" title="E83">A10</font></i></a>, <a class="txt" href="complex2.html#E17:88"><i><font color="Green" title="E86">A13</font></i></a>, <a class="txt" href="complex2.html#E27:88"><i><font color="Green" title="E95">A22</font></i></a>, <a class="txt" href="complex2.html#E28:88"><i><font color="Green" title="E96">A23</font></i></a></i>
;<br/>

<b>thus </b><a NAME="E30:88"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex2.html#K4" title="COMPLEX2:func.4">angle</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</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#E22:88"><i><font color="Green" title="E91">A18</font></i></a>, <a class="ref" href="complex2.html#D6" target="_self" title="COMPLEX2:def.6">Def6</a></i>;<br/>

<b>thus </b><a NAME="E31:88"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="complex2.html#E3:88"><i><font color="Green" title="E76">A3</font></i></a>, <a class="txt" href="complex2.html#E5:88"><i><font color="Green" title="E77">A4</font></i></a>, <a class="txt" href="complex2.html#E19:88"><i><font color="Green" title="E88">A15</font></i></a>, <a class="txt" href="complex2.html#E22:88"><i><font color="Green" title="E91">A18</font></i></a>, <a class="txt" href="complex2.html#E23:88"><i><font color="Green" title="E92">A19</font></i></a>, <a class="txt" href="complex2.html#E29:88"><i><font color="Green" title="E97">A24</font></i></a>, <a class="ref" href="xcmplx_1.html#T3" title="XCMPLX_1:th.3">XCMPLX_1:3</a></i>;<br/>


</div>
