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      <margins left="39" right="39" top="39" bottom="39" />
      <header alignment="Center" color="#a9a9a9">&amp;[DATE] &amp;[TIME] - &amp;[FILENAME]</header>
      <footer alignment="Center" color="#a9a9a9">&amp;[PAGENUM] / &amp;[COUNT]</footer>
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  <region id="0" left="63" top="9" width="78" height="50" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">1</e>
        <e type="operand">i</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">/</e>
      </input>
      <result action="numeric">
        <e type="operand">1</e>
        <e type="operator" args="1">-</e>
      </result>
    </math>
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  <region id="1" left="234" top="18" width="77" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">i</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
      </input>
      <result action="symbolic">
        <e type="operand">1</e>
        <e type="operator" args="1">-</e>
      </result>
    </math>
  </region>
  <region id="2" left="486" top="27" width="66" height="41" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">1</e>
        <e type="operand">i</e>
        <e type="operator" args="2">/</e>
      </input>
      <result action="numeric">
        <e type="operand">i</e>
        <e type="operator" args="1">-</e>
      </result>
    </math>
  </region>
  <region id="3" left="63" top="54" width="85" height="41" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">1</e>
        <e type="operand">i</e>
        <e type="operator" args="2">/</e>
        <e type="operand">1</e>
        <e type="operand">i</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">*</e>
      </input>
      <result action="numeric">
        <e type="operand">1</e>
        <e type="operator" args="1">-</e>
      </result>
    </math>
  </region>
  <region id="4" left="135" top="63" width="208" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="spa">
      <p>Numeric method is right.</p>
    </text>
  </region>
  <region id="5" left="486" top="63" width="111" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">i</e>
        <e type="operator" args="1">-</e>
        <e type="bracket">(</e>
        <e type="operand">i</e>
        <e type="operator" args="1">-</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">*</e>
      </input>
      <result action="numeric">
        <e type="operand">1</e>
        <e type="operator" args="1">-</e>
      </result>
    </math>
  </region>
  <region id="6" left="63" top="99" width="76" height="41" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">1</e>
        <e type="operand">i</e>
        <e type="operator" args="2">/</e>
        <e type="operand">1</e>
        <e type="operand">i</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">*</e>
      </input>
      <result action="symbolic">
        <e type="operand">1</e>
      </result>
    </math>
  </region>
  <region id="7" left="135" top="108" width="216" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="spa">
      <p>Symbolic method is wrong.</p>
    </text>
  </region>
  <region id="8" left="9" top="135" width="451" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="spa">
      <p>Math books show the next definition for the imaginary numbers product.</p>
    </text>
  </region>
  <region id="9" left="9" top="171" width="362" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="spa">
      <p>For the real numbers a,b with a&gt;0 and b&gt;0: </p>
    </text>
  </region>
  <region id="10" left="9" top="198" width="140" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">a</e>
        <e type="operator" args="1">-</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operand">b</e>
        <e type="operator" args="1">-</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operator" args="2">*</e>
        <e type="operand">a</e>
        <e type="operand">b</e>
        <e type="operator" args="2">*</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operator" args="1">-</e>
        <e type="operator" args="2">≡</e>
      </input>
    </math>
  </region>
  <region id="11" left="9" top="225" width="415" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="spa">
      <p>because now we are dealing with imaginary numbers</p>
    </text>
  </region>
  <region id="12" left="9" top="252" width="93" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">a</e>
        <e type="operator" args="1">-</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operand">a</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">≡</e>
      </input>
    </math>
  </region>
  <region id="13" left="9" top="279" width="93" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">b</e>
        <e type="operator" args="1">-</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operand">b</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">≡</e>
      </input>
    </math>
  </region>
  <region id="14" left="9" top="306" width="37" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="spa">
      <p>and</p>
    </text>
  </region>
  <region id="15" left="9" top="324" width="245" height="34" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">a</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="bracket">(</e>
        <e type="operand">b</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">*</e>
        <e type="operand">a</e>
        <e type="operand">b</e>
        <e type="operator" args="2">*</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operand">i</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">≡</e>
        <e type="operand">a</e>
        <e type="operand">b</e>
        <e type="operator" args="2">*</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operator" args="1">-</e>
        <e type="operator" args="2">≡</e>
      </input>
    </math>
  </region>
  <region id="16" left="9" top="360" width="28" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="spa">
      <p>so</p>
    </text>
  </region>
  <region id="17" left="9" top="387" width="165" height="28" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">a</e>
        <e type="operator" args="1">-</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operand">b</e>
        <e type="operator" args="1">-</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operator" args="2">*</e>
        <e type="operand">a</e>
        <e type="operator" args="1">-</e>
        <e type="bracket">(</e>
        <e type="operand">b</e>
        <e type="operator" args="1">-</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">*</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operator" args="2">≠</e>
      </input>
    </math>
  </region>
  <region id="18" left="9" top="414" width="131" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">a</e>
        <e type="operator" args="1">-</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operand">b</e>
        <e type="operator" args="1">-</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operator" args="2">*</e>
        <e type="operand">a</e>
        <e type="operand">b</e>
        <e type="operator" args="2">*</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operator" args="2">≠</e>
      </input>
    </math>
  </region>
  <region id="19" left="9" top="441" width="86" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="spa">
      <p>Examples:</p>
    </text>
  </region>
  <region id="20" left="9" top="468" width="123" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">4</e>
        <e type="operator" args="1">-</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operand">4</e>
        <e type="operator" args="1">-</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operator" args="2">*</e>
      </input>
      <result action="numeric">
        <e type="operand">4</e>
        <e type="operator" args="1">-</e>
      </result>
    </math>
  </region>
  <region id="21" left="153" top="468" width="100" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">4</e>
        <e type="operand">4</e>
        <e type="operator" args="2">*</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operator" args="1">-</e>
      </input>
      <result action="numeric">
        <e type="operand">4</e>
        <e type="operator" args="1">-</e>
      </result>
    </math>
  </region>
  <region id="22" left="9" top="495" width="198" height="28" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">4</e>
        <e type="operator" args="1">-</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operand">4</e>
        <e type="operator" args="1">-</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operator" args="2">*</e>
        <e type="operand">4</e>
        <e type="operator" args="1">-</e>
        <e type="bracket">(</e>
        <e type="operand">4</e>
        <e type="operator" args="1">-</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">*</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operator" args="2">≡</e>
      </input>
      <result action="numeric">
        <e type="operand">0</e>
      </result>
    </math>
  </region>
  <region id="23" left="216" top="495" width="70" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="spa">
      <p>False=0</p>
    </text>
  </region>
  <region id="24" left="9" top="531" width="173" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">4</e>
        <e type="operator" args="1">-</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operand">4</e>
        <e type="operator" args="1">-</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operator" args="2">*</e>
        <e type="operand">4</e>
        <e type="operand">4</e>
        <e type="operator" args="2">*</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operator" args="1">-</e>
        <e type="operator" args="2">≡</e>
      </input>
      <result action="numeric">
        <e type="operand">1</e>
      </result>
    </math>
  </region>
  <region id="25" left="216" top="531" width="61" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="spa">
      <p>True=1</p>
    </text>
  </region>
  <region id="26" left="9" top="567" width="96" height="37" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">4</e>
        <e type="operator" args="1">-</e>
        <e type="bracket">(</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="function" preserve="true" args="1">sqrt</e>
      </input>
      <result action="numeric">
        <e type="operand">4</e>
      </result>
    </math>
  </region>
  <region id="27" left="9" top="612" width="538" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="spa">
      <p>There are some problems with the symbolic method interpretation:</p>
    </text>
  </region>
  <region id="28" left="9" top="639" width="142" height="43" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">2</e>
        <e type="operand">3</e>
        <e type="operator" args="2">/</e>
        <e type="operand">π</e>
        <e type="operator" args="2">*</e>
        <e type="function" preserve="true" args="1">sin</e>
      </input>
      <result action="numeric">
        <e type="operand">0.866</e>
      </result>
    </math>
  </region>
  <region id="29" left="9" top="693" width="151" height="43" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">4</e>
        <e type="operand">3</e>
        <e type="operator" args="2">/</e>
        <e type="operand">π</e>
        <e type="operator" args="2">*</e>
        <e type="function" preserve="true" args="1">sin</e>
      </input>
      <result action="numeric">
        <e type="operand">0.866</e>
        <e type="operator" args="1">-</e>
      </result>
    </math>
  </region>
  <region id="30" left="9" top="738" width="296" height="61" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">2</e>
        <e type="operand">3</e>
        <e type="operator" args="2">/</e>
        <e type="operand">π</e>
        <e type="operator" args="2">*</e>
        <e type="function" preserve="true" args="1">sin</e>
        <e type="operand">4</e>
        <e type="operand">3</e>
        <e type="operator" args="2">/</e>
        <e type="operand">π</e>
        <e type="operator" args="2">*</e>
        <e type="function" preserve="true" args="1">sin</e>
        <e type="operator" args="2">+</e>
      </input>
      <result action="symbolic">
        <e type="operand">3</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operand">2</e>
        <e type="operand">4</e>
        <e type="operand">π</e>
        <e type="operator" args="2">*</e>
        <e type="operand">3</e>
        <e type="operator" args="2">/</e>
        <e type="function" preserve="true" args="1">sin</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="operand">2</e>
        <e type="operator" args="2">/</e>
      </result>
    </math>
  </region>
  <region id="31" left="9" top="819" width="215" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="spa">
      <p>It must be equal to zero.</p>
    </text>
  </region>
  <region id="32" left="9" top="864" width="279" height="43" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">2</e>
        <e type="operand">3</e>
        <e type="operator" args="2">/</e>
        <e type="operand">π</e>
        <e type="operator" args="2">*</e>
        <e type="function" preserve="true" args="1">sin</e>
        <e type="operand">4</e>
        <e type="operand">3</e>
        <e type="operator" args="2">/</e>
        <e type="operand">π</e>
        <e type="operator" args="2">*</e>
        <e type="function" preserve="true" args="1">sin</e>
        <e type="operator" args="2">+</e>
      </input>
      <result action="numeric">
        <e type="operand">3.3307</e>
        <e type="operand">10</e>
        <e type="operand">16</e>
        <e type="operator" args="1">-</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
      </result>
    </math>
  </region>
</regions>