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      <revision>5</revision>
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    <metadata lang="eng">
      <author>Lee Curtis Snook</author>
    </metadata>
    <calculation>
      <precision>4</precision>
      <exponentialThreshold>5</exponentialThreshold>
      <trailingZeros>false</trailingZeros>
      <significantDigitsMode>false</significantDigitsMode>
      <roundingMode>0</roundingMode>
      <approximateEqualAccuracy>0</approximateEqualAccuracy>
      <fractions>decimal</fractions>
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      <paper id="1" orientation="Portrait" width="850" height="1100" />
      <margins left="39" right="39" top="49" bottom="49" />
      <header alignment="Center" color="#a9a9a9">&amp;[DATE] &amp;[TIME] - &amp;[FILENAME]</header>
      <footer alignment="Center" color="#a9a9a9">&amp;[PAGENUM] / &amp;[COUNT]</footer>
      <backgrounds />
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    <region left="27" top="27" width="411" height="25" color="#000000" fontSize="10">
      <text lang="eng" width="411" fontFamily="Arial" fontSize="10">
        <content>
          <p>Example 1; alpha = 0, Output should be \[REGION[aab759884e01448282adc49745cf3b7e]]\ which it is;</p>
        </content>
        <regions>
          <region id="aab759884e01448282adc49745cf3b7e" left="240" top="0" width="52" height="24" color="#000000" fontSize="10">
            <math>
              <input>
                <e type="operand">1</e>
                <e type="operand">i0</e>
                <e type="operator" args="2">+</e>
              </input>
            </math>
          </region>
        </regions>
      </text>
    </region>
    <region left="18" top="72" width="61" height="27" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">α</e>
          <e type="operand">0</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="function" args="3">mat</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="252" top="72" width="59" height="27" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">α</e>
        </input>
        <result action="numeric">
          <e type="operand">0</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="function" args="3">mat</e>
        </result>
      </math>
    </region>
    <region left="18" top="99" width="129" height="69" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">P</e>
          <e type="operand">i</e>
          <e type="operand">α</e>
          <e type="operator" args="2">*</e>
          <e type="bracket">(</e>
          <e type="operand">n</e>
          <e type="operator" args="2">^</e>
          <e type="operand">n</e>
          <e type="operator" args="1">!</e>
          <e type="operator" args="2">/</e>
          <e type="operand">n</e>
          <e type="operand">0</e>
          <e type="operand">16</e>
          <e type="function" args="4">sum</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="252" top="126" width="94" height="36" color="#000000" fontSize="10">
      <math decimalPlaces="1" significantDigitsMode="true" exponentialThreshold="0" trailingZeros="true" ignoreUnits="true">
        <input>
          <e type="operand">P</e>
        </input>
        <result action="numeric">
          <e type="operand">1</e>
          <e type="operand">10</e>
          <e type="operand">0</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">*</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="function" args="3">mat</e>
        </result>
      </math>
    </region>
    <region left="18" top="180" width="79" height="26" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">x</e>
          <e type="operand">P</e>
          <e type="function" args="1">Re</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="252" top="180" width="79" height="26" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">y</e>
          <e type="operand">P</e>
          <e type="function" args="1">Im</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="18" top="234" width="59" height="27" color="#000000" bgColor="#ffff80" fontSize="10">
      <math>
        <input>
          <e type="operand">x</e>
        </input>
        <result action="numeric">
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="function" args="3">mat</e>
        </result>
      </math>
    </region>
    <region left="144" top="234" width="58" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Arial" fontSize="10">
        <content>
          <p>Correct</p>
        </content>
      </text>
    </region>
    <region left="252" top="234" width="59" height="27" color="#000000" bgColor="#ffff80" fontSize="10">
      <math>
        <input>
          <e type="operand">y</e>
        </input>
        <result action="numeric">
          <e type="operand">0</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="function" args="3">mat</e>
        </result>
      </math>
    </region>
    <region left="0" top="288" width="476" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Arial" fontSize="10">
        <content>
          <p>--------------------------------------------------------------------------------------------------------</p>
        </content>
      </text>
    </region>
    <region left="36" top="315" width="375" height="25" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Arial" fontSize="10">
        <content>
          <p>Example 2; alpha =π Output should be  \[REGION[d83a2f66e4dd4cda85232d20ca626480]]\0, which it is;</p>
        </content>
        <regions>
          <region id="d83a2f66e4dd4cda85232d20ca626480" left="238" top="0" width="55" height="24" color="#000000" fontSize="10">
            <math>
              <input>
                <e type="operand">1</e>
                <e type="operator" args="1">-</e>
                <e type="operand">i</e>
                <e type="operator" args="2">+</e>
              </input>
            </math>
          </region>
        </regions>
      </text>
    </region>
    <region left="36" top="351" width="61" height="27" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">α</e>
          <e type="operand">π</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="function" args="3">mat</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="243" top="351" width="99" height="27" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">α</e>
        </input>
        <result action="numeric">
          <e type="operand">3.1416</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="function" args="3">mat</e>
        </result>
      </math>
    </region>
    <region left="36" top="396" width="129" height="69" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">P</e>
          <e type="operand">i</e>
          <e type="operand">α</e>
          <e type="operator" args="2">*</e>
          <e type="bracket">(</e>
          <e type="operand">n</e>
          <e type="operator" args="2">^</e>
          <e type="operand">n</e>
          <e type="operator" args="1">!</e>
          <e type="operator" args="2">/</e>
          <e type="operand">n</e>
          <e type="operand">0</e>
          <e type="operand">16</e>
          <e type="function" args="4">sum</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="243" top="414" width="193" height="36" color="#000000" fontSize="10">
      <math decimalPlaces="1" significantDigitsMode="true" exponentialThreshold="0" trailingZeros="true" ignoreUnits="true">
        <input>
          <e type="operand">P</e>
        </input>
        <result action="numeric">
          <e type="operand">1</e>
          <e type="operand">10</e>
          <e type="operand">0</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="1">-</e>
          <e type="operand">8</e>
          <e type="operand">10</e>
          <e type="operand">7</e>
          <e type="operator" args="1">-</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">*</e>
          <e type="operand">i</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">-</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="function" args="3">mat</e>
        </result>
      </math>
    </region>
    <region left="252" top="468" width="79" height="26" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">y</e>
          <e type="operand">P</e>
          <e type="function" args="1">Im</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="36" top="477" width="79" height="26" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">x</e>
          <e type="operand">P</e>
          <e type="function" args="1">Re</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="36" top="504" width="72" height="27" color="#000000" bgColor="#ffff80" fontSize="10">
      <math>
        <input>
          <e type="operand">x</e>
        </input>
        <result action="numeric">
          <e type="operand">1</e>
          <e type="operator" args="1">-</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="function" args="3">mat</e>
        </result>
      </math>
    </region>
    <region left="135" top="504" width="58" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Arial" fontSize="10">
        <content>
          <p>Correct</p>
        </content>
      </text>
    </region>
    <region left="252" top="504" width="59" height="27" color="#000000" bgColor="#ffff80" fontSize="10">
      <math decimalPlaces="0" exponentialThreshold="10" ignoreUnits="true">
        <description active="false" position="Top" lang="eng" />
        <input>
          <e type="operand">y</e>
        </input>
        <result action="numeric">
          <e type="operand">0</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="function" args="3">mat</e>
        </result>
      </math>
    </region>
    <region left="0" top="549" width="476" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Arial" fontSize="10">
        <content>
          <p>--------------------------------------------------------------------------------------------------------</p>
        </content>
      </text>
    </region>
    <region left="36" top="567" width="366" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Arial" fontSize="10">
        <content>
          <p>Example 3; Now set up a range of values for alpha, 0 and π</p>
        </content>
      </text>
    </region>
    <region left="63" top="594" width="50" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Arial" fontSize="10">
        <content>
          <p>Matrix</p>
        </content>
      </text>
    </region>
    <region left="270" top="594" width="187" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Arial" fontSize="10">
        <content>
          <p>Try Matrix or Range Methods</p>
        </content>
      </text>
    </region>
    <region left="576" top="594" width="53" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Arial" fontSize="10">
        <content>
          <p>Range</p>
        </content>
      </text>
    </region>
    <region left="36" top="612" width="61" height="45" color="#000000" fontSize="10">
      <math evaluate="false">
        <input>
          <e type="operand">α</e>
          <e type="operand">0</e>
          <e type="operand">π</e>
          <e type="operand">2</e>
          <e type="operand">1</e>
          <e type="function" args="4">mat</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="144" top="612" width="99" height="45" color="#000000" fontSize="10">
      <math evaluate="false">
        <input>
          <e type="operand">α</e>
        </input>
        <result action="numeric">
          <e type="operand">0</e>
          <e type="operand">3.1416</e>
          <e type="operand">2</e>
          <e type="operand">1</e>
          <e type="function" args="4">mat</e>
        </result>
      </math>
    </region>
    <region left="639" top="621" width="99" height="27" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">α</e>
        </input>
        <result action="numeric">
          <e type="operand">3.1416</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="function" args="3">mat</e>
        </result>
      </math>
    </region>
    <region left="495" top="630" width="102" height="26" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">α</e>
          <e type="operand">0</e>
          <e type="operand">π</e>
          <e type="operand">π</e>
          <e type="function" args="3">range</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="27" top="666" width="129" height="69" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">P</e>
          <e type="operand">i</e>
          <e type="operand">α</e>
          <e type="operator" args="2">*</e>
          <e type="bracket">(</e>
          <e type="operand">n</e>
          <e type="operator" args="2">^</e>
          <e type="operand">n</e>
          <e type="operator" args="1">!</e>
          <e type="operator" args="2">/</e>
          <e type="operand">n</e>
          <e type="operand">0</e>
          <e type="operand">16</e>
          <e type="function" args="4">sum</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="234" top="684" width="193" height="63" color="#000000" fontSize="10">
      <math decimalPlaces="1" significantDigitsMode="true" exponentialThreshold="0" trailingZeros="true" ignoreUnits="true">
        <input>
          <e type="operand">P</e>
        </input>
        <result action="numeric">
          <e type="operand">1</e>
          <e type="operand">10</e>
          <e type="operand">0</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="1">-</e>
          <e type="operand">2</e>
          <e type="operand">10</e>
          <e type="operand">0</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="1">-</e>
          <e type="operand">8</e>
          <e type="operand">10</e>
          <e type="operand">7</e>
          <e type="operator" args="1">-</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">*</e>
          <e type="operand">i</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">-</e>
          <e type="operand">2</e>
          <e type="operand">1</e>
          <e type="function" args="4">mat</e>
        </result>
      </math>
    </region>
    <region left="36" top="774" width="79" height="26" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">x</e>
          <e type="operand">P</e>
          <e type="function" args="1">Re</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="234" top="774" width="79" height="26" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">y</e>
          <e type="operand">P</e>
          <e type="function" args="1">Im</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="36" top="819" width="72" height="45" color="#000000" bgColor="#ffff80" fontSize="10">
      <math>
        <input>
          <e type="operand">x</e>
        </input>
        <result action="numeric">
          <e type="operand">1</e>
          <e type="operator" args="1">-</e>
          <e type="operand">2</e>
          <e type="operator" args="1">-</e>
          <e type="operand">2</e>
          <e type="operand">1</e>
          <e type="function" args="4">mat</e>
        </result>
      </math>
    </region>
    <region left="225" top="819" width="59" height="45" color="#000000" bgColor="#ffff80" fontSize="10">
      <math decimalPlaces="0" exponentialThreshold="10" ignoreUnits="true">
        <description active="false" position="Top" lang="eng" />
        <input>
          <e type="operand">y</e>
        </input>
        <result action="numeric">
          <e type="operand">0</e>
          <e type="operand">0</e>
          <e type="operand">2</e>
          <e type="operand">1</e>
          <e type="function" args="4">mat</e>
        </result>
      </math>
    </region>
    <region left="342" top="828" width="267" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Arial" fontSize="10">
        <content>
          <p>x and y values don't match examples 1 &amp; 2</p>
        </content>
      </text>
    </region>
  </regions>
</worksheet>