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      <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="18" top="18" width="135" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p bold="true">Komplexe Zahlen</p>
    </text>
    <text lang="eng">
      <p bold="true">Complex Numbers</p>
    </text>
  </region>
  <region id="1" left="576" top="18" width="94" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Mathematik.sm">Mathematik</p>
    </text>
    <text lang="eng">
      <p href="Mathematik.sm">Mathematics</p>
    </text>
  </region>
  <region id="2" left="576" top="36" width="61" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Handbook.sm">Inhalt</p>
    </text>
    <text lang="eng">
      <p href="Handbook.sm">Contents</p>
    </text>
  </region>
  <region id="3" left="18" top="63" width="645" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Zur Darstellung komplexer Zahlen wird die imaginäre Einheit i verwendet.
Das ist ein gewöhnlicher Bezeichner, der mit der Wurzel aus -1 vorbelegt ist.</p>
    </text>
    <text lang="eng">
      <p>Complex numbers are represented using the imaginary unit i. This is an
ordinary variable name, pre-defined as square root of -1.</p>
    </text>
  </region>
  <region id="4" left="18" top="126" width="88" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">z.1</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="5" left="126" top="126" width="83" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">z.1</e>
      </input>
      <result action="numeric">
        <e type="operand">3</e>
        <e type="operand">i</e>
        <e type="operator" args="2">+</e>
      </result>
    </math>
  </region>
  <region id="6" left="18" top="162" width="101" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">z.2</e>
        <e type="operand">3</e>
        <e type="operand" style="unit">m</e>
        <e type="operator" args="2">*</e>
        <e type="operand">i</e>
        <e type="operand" style="unit">s</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="7" left="126" top="162" width="62" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math error="74">
      <input>
        <e type="operand">z.2</e>
      </input>
      <result action="numeric">
        <e type="operand">#</e>
      </result>
    </math>
  </region>
  <region id="8" left="288" top="162" width="402" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Die Einheiten von Real- und Imaginärteil müssen 
übereinstimmen.</p>
    </text>
    <text lang="eng">
      <p>Units of real and imaginary part must match.</p>
    </text>
  </region>
  <region id="9" left="18" top="216" width="101" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">z.3</e>
        <e type="operand">3</e>
        <e type="operand" style="unit">m</e>
        <e type="operator" args="2">*</e>
        <e type="operand">i</e>
        <e type="operand" style="unit">m</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="10" left="126" top="216" width="105" height="33" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">z.3</e>
      </input>
      <result action="numeric">
        <e type="operand">3</e>
        <e type="operand">i</e>
        <e type="operator" args="2">+</e>
        <e type="bracket">(</e>
        <e type="operand" style="unit">m</e>
        <e type="operator" args="2">*</e>
      </result>
    </math>
  </region>
  <region id="11" left="288" top="216" width="423" height="56" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Bei der Anzeige komplexer Zahlen mit Maßeinheiten
wird korrekt die Klammer um Real- und Imaginärteil
gesetz.</p>
    </text>
    <text lang="eng">
      <p>SMath sets correct brackets when displaying 
complex numbers with units...</p>
    </text>
  </region>
  <region id="12" left="126" top="270" width="142" height="32" color="#ff0000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">z.3</e>
      </input>
      <contract>
        <e type="operand" style="unit">cm</e>
      </contract>
      <result action="numeric">
        <e type="operand">300</e>
        <e type="operand">100</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
      </result>
    </math>
  </region>
  <region id="13" left="288" top="270" width="414" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Wird die Maßeinheit verändert, vergisst SMath die
Klammer</p>
    </text>
    <text lang="eng">
      <p>as long as you do not change that unit.</p>
    </text>
  </region>
  <region id="14" left="18" top="306" width="619" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Viele Funktionen für komplexe Zahlen funktionieren nicht mit Maßeinheiten.</p>
    </text>
    <text lang="eng">
      <p>Some of the functions for complex numbers don't work with units.</p>
    </text>
  </region>
  <region id="15" left="324" top="333" width="296" height="72" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Die Betragsfunktion wird als abs() 
eingegeben oder aus der 
Arithmetik-Palette der 
Seitenleiste gewählt.</p>
    </text>
    <text lang="eng">
      <p>The absolute value function is 
input as abs() or choosen from
the Arithmetics palette of the
side panel.</p>
    </text>
  </region>
  <region id="16" left="18" top="342" width="83" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">z.1</e>
      </input>
      <result action="numeric">
        <e type="operand">3</e>
        <e type="operand">i</e>
        <e type="operator" args="2">+</e>
      </result>
    </math>
  </region>
  <region id="17" left="189" top="342" width="105" height="33" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">z.3</e>
      </input>
      <result action="numeric">
        <e type="operand">3</e>
        <e type="operand">i</e>
        <e type="operator" args="2">+</e>
        <e type="bracket">(</e>
        <e type="operand" style="unit">m</e>
        <e type="operator" args="2">*</e>
      </result>
    </math>
  </region>
  <region id="18" left="18" top="378" width="90" height="34" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">z.1</e>
        <e type="function" preserve="true" args="1">Re</e>
      </input>
      <result action="numeric">
        <e type="operand">3</e>
      </result>
    </math>
  </region>
  <region id="19" left="189" top="378" width="90" height="34" color="#000000" bgColor="#ffffff" fontSize="10">
    <math error="79">
      <input>
        <e type="operand">z.3</e>
        <e type="function" preserve="true" args="1">Re</e>
      </input>
      <result action="numeric">
        <e type="operand">#</e>
      </result>
    </math>
  </region>
  <region id="20" left="333" top="405" width="154" height="111" color="#000000" bgColor="#ffffff">
    <picture>
      <raw format="png" encoding="base64"> </raw>
    </picture>
  </region>
  <region id="21" left="18" top="414" width="90" height="34" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">z.1</e>
        <e type="function" preserve="true" args="1">Im</e>
      </input>
      <result action="numeric">
        <e type="operand">1</e>
      </result>
    </math>
  </region>
  <region id="22" left="189" top="414" width="90" height="34" color="#000000" bgColor="#ffffff" fontSize="10">
    <math error="79">
      <input>
        <e type="operand">z.3</e>
        <e type="function" preserve="true" args="1">Im</e>
      </input>
      <result action="numeric">
        <e type="operand">#</e>
      </result>
    </math>
  </region>
  <region id="23" left="522" top="414" width="20" height="24" border="true" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">X</e>
      </input>
    </math>
  </region>
  <region id="24" left="549" top="414" width="20" height="24" border="true" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>:</p>
    </text>
  </region>
  <region id="25" left="576" top="414" width="61" height="24" border="true" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Strg-M</p>
    </text>
  </region>
  <region id="26" left="18" top="450" width="151" height="34" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">z.1</e>
        <e type="function" preserve="true" args="1">arg</e>
      </input>
      <contract>
        <e type="operand" style="unit">°</e>
      </contract>
      <result action="numeric">
        <e type="operand">18.4349</e>
      </result>
    </math>
  </region>
  <region id="27" left="189" top="450" width="101" height="34" color="#000000" bgColor="#ffffff" fontSize="10">
    <math error="79">
      <input>
        <e type="operand">z.3</e>
        <e type="function" preserve="true" args="1">arg</e>
      </input>
      <contract>
        <e type="operand" style="unit">°</e>
      </contract>
      <result action="numeric">
        <e type="operand">#</e>
      </result>
    </math>
  </region>
  <region id="28" left="18" top="486" width="109" height="34" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">z.1</e>
        <e type="function" preserve="true" args="1">abs</e>
      </input>
      <result action="numeric">
        <e type="operand">3.1623</e>
      </result>
    </math>
  </region>
  <region id="29" left="189" top="486" width="123" height="34" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">z.3</e>
        <e type="function" preserve="true" args="1">abs</e>
      </input>
      <result action="numeric">
        <e type="operand">3.1623</e>
        <e type="operand" style="unit">m</e>
        <e type="operator" args="2">*</e>
      </result>
    </math>
  </region>
  <region id="30" left="18" top="522" width="690" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Die komplexe Konjugation fehlt als Funktion oder Operator. Abhilfe kann man selbst 
schaffen:</p>
    </text>
  </region>
  <region id="31" left="18" top="558" width="110" height="52" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">z</e>
        <e type="function" args="1">conj</e>
        <e type="operand">z</e>
        <e type="function" preserve="true" args="1">abs</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operand">z</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="32" left="18" top="612" width="90" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p bold="true">Polarform </p>
    </text>
    <text lang="eng">
      <p bold="true">Polar representation</p>
    </text>
  </region>
  <region id="33" left="18" top="639" width="728" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Die Polarform kann nur bei der Definition, nicht jedoch bei der Anzeige benutzt werden.</p>
    </text>
    <text lang="eng">
      <p>The polar form can be used for definition but not for display.</p>
    </text>
  </region>
  <region id="34" left="18" top="666" width="240" height="71" color="#000000" bgColor="#ffffff" fontSize="10">
    <plot type="2d" render="lines" scale_x="0.531441" scale_y="0.531441" scale_z="0.531441" rotate_x="0" rotate_y="0" rotate_z="0" transpose_x="0" transpose_y="0" transpose_z="0">
      <input>
        <e type="operand">e</e>
        <e type="operand">i</e>
        <e type="operand">x</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">^</e>
        <e type="function" preserve="true" args="1">Re</e>
      </input>
    </plot>
  </region>
  <region id="35" left="270" top="666" width="240" height="71" color="#000000" bgColor="#ffffff" fontSize="10">
    <plot type="2d" render="lines" scale_x="0.531441" scale_y="0.531441" scale_z="0.531441" rotate_x="0" rotate_y="0" rotate_z="0" transpose_x="0" transpose_y="0" transpose_z="0">
      <input>
        <e type="operand">e</e>
        <e type="operand">i</e>
        <e type="operand">x</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">^</e>
        <e type="function" preserve="true" args="1">Im</e>
      </input>
    </plot>
  </region>
  <region id="36" left="18" top="792" width="83" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">z.1</e>
      </input>
      <result action="numeric">
        <e type="operand">3</e>
        <e type="operand">i</e>
        <e type="operator" args="2">+</e>
      </result>
    </math>
  </region>
  <region id="37" left="108" top="792" width="109" height="34" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">z.1</e>
        <e type="function" preserve="true" args="1">abs</e>
      </input>
      <result action="numeric">
        <e type="operand">3.1623</e>
      </result>
    </math>
  </region>
  <region id="38" left="243" top="792" width="140" height="34" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">z.1</e>
        <e type="function" preserve="true" args="1">arg</e>
      </input>
      <result action="numeric">
        <e type="operand">0.3218</e>
      </result>
    </math>
  </region>
  <region id="39" left="396" top="792" width="151" height="34" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">z.1</e>
        <e type="function" preserve="true" args="1">arg</e>
      </input>
      <contract>
        <e type="operand" style="unit">°</e>
      </contract>
      <result action="numeric">
        <e type="operand">18.4349</e>
      </result>
    </math>
  </region>
  <region id="40" left="18" top="828" width="262" height="44" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">z.1</e>
        <e type="function" preserve="true" args="1">Re</e>
        <e type="operand">z.1</e>
        <e type="function" preserve="true" args="1">Im</e>
        <e type="function" preserve="true" args="2">xy2pol</e>
      </input>
      <result action="numeric">
        <e type="operand">3.1623</e>
        <e type="operand">0.3218</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">sys</e>
      </result>
    </math>
  </region>
  <region id="41" left="360" top="828" width="65" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Radius </p>
    </text>
    <text lang="eng">
      <p>radius</p>
    </text>
  </region>
  <region id="42" left="360" top="846" width="115" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Phasenwinkel </p>
    </text>
    <text lang="eng">
      <p>argument</p>
    </text>
  </region>
  <region id="43" left="18" top="873" width="337" height="62" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">z.1</e>
        <e type="function" preserve="true" args="1">abs</e>
        <e type="operand">z.1</e>
        <e type="function" preserve="true" args="1">arg</e>
        <e type="function" preserve="true" args="2">pol2xy</e>
      </input>
      <result action="numeric">
        <e type="operand">3</e>
        <e type="operand">1.0895</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>
        <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">3.2685</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>
        <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" preserve="true" args="4">sys</e>
      </result>
    </math>
  </region>
  <region id="44" left="360" top="882" width="82" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Realteil </p>
    </text>
    <text lang="eng">
      <p>real part</p>
    </text>
  </region>
  <region id="45" left="360" top="909" width="115" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Imaginärteil </p>
    </text>
    <text lang="eng">
      <p>imaginary part</p>
    </text>
  </region>
  <region id="46" left="18" top="945" width="176" height="51" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">z.1</e>
      </input>
      <contract>
        <e type="operand">e</e>
        <e type="operand">i</e>
        <e type="operand">z.1</e>
        <e type="function" preserve="true" args="1">arg</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">^</e>
      </contract>
      <result action="numeric">
        <e type="operand">3.1623</e>
      </result>
    </math>
  </region>
  <region id="47" left="315" top="945" width="93" height="43" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">e</e>
        <e type="operand">i</e>
        <e type="operand">z.1</e>
        <e type="function" preserve="true" args="1">arg</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">^</e>
      </input>
    </math>
  </region>
  <region id="48" left="414" top="963" width="254" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>wurde  hier als Maßeinheit bei
der Anzeige verwendet.</p>
    </text>
    <text lang="eng">
      <p>has been used as unit for display</p>
    </text>
  </region>
  <region id="49" left="18" top="999" width="248" height="41" color="#ff0000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">z.1</e>
      </input>
      <contract>
        <e type="operand">e</e>
        <e type="operand">i</e>
        <e type="operand">0.3218</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">^</e>
      </contract>
      <result action="numeric">
        <e type="operand">3.1623</e>
        <e type="operand">0.0002</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">-</e>
      </result>
    </math>
  </region>
  <region id="50" left="315" top="1008" width="401" height="40" color="#ff0000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Vorsicht, in diesem Fall ist das Klammerproblem 
nicht offensichtlich!</p>
    </text>
    <text lang="eng">
      <p>Caution, in this case the missing bracket error 
is not obvious</p>
    </text>
  </region>
  <region id="51" left="18" top="1053" width="234" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Animation des Phasenwinkels</p>
    </text>
    <text lang="eng">
      <p>Animation of the angle</p>
    </text>
  </region>
  <region id="52" left="18" top="1071" width="94" height="41" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">z.2</e>
        <e type="operand">r</e>
        <e type="operand">e</e>
        <e type="operand">i</e>
        <e type="operand">φ</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="53" left="171" top="1107" width="151" height="41" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">α</e>
        <e type="operand">π</e>
        <e type="operand">20</e>
        <e type="operator" args="2">/</e>
        <e type="operand">2</e>
        <e type="operand">π</e>
        <e type="operator" args="2">*</e>
        <e type="operand">2</e>
        <e type="operand">π</e>
        <e type="operand">20</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">*</e>
        <e type="function" preserve="true" args="3">range</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="54" left="27" top="1116" width="43" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">r</e>
        <e type="operand">2</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="55" left="126" top="1116" width="43" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">φ</e>
        <e type="operand">t</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="56" left="333" top="1116" width="114" height="34" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">cz.2</e>
        <e type="operand">z.2</e>
        <e type="function" args="1">conj</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="57" left="18" top="1152" width="240" height="158" color="#000000" bgColor="#ffffff" fontSize="10">
    <plot type="2d" render="lines" scale_x="2.8245855390489" scale_y="2.8245855390489" scale_z="2.8245855390489" rotate_x="0" rotate_y="0" rotate_z="0" transpose_x="5" transpose_y="-5" transpose_z="0" animate="α" frameRate="20">
      <input>
        <e type="operand">z.2</e>
        <e type="function" preserve="true" args="1">Re</e>
        <e type="operand">z.2</e>
        <e type="function" preserve="true" args="1">Im</e>
        <e type="operand" style="string">.</e>
        <e type="operand">20</e>
        <e type="operand" style="string">red</e>
        <e type="operand">1</e>
        <e type="operand">5</e>
        <e type="function" preserve="true" args="7">mat</e>
        <e type="operand">cz.2</e>
        <e type="function" preserve="true" args="1">Re</e>
        <e type="operand">cz.2</e>
        <e type="function" preserve="true" args="1">Im</e>
        <e type="operand" style="string">.</e>
        <e type="operand">20</e>
        <e type="operand" style="string">green</e>
        <e type="operand">1</e>
        <e type="operand">5</e>
        <e type="function" preserve="true" args="7">mat</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">sys</e>
      </input>
    </plot>
  </region>
  <region id="58" left="18" top="1395" width="136" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p bold="true">Überlebensregel</p>
    </text>
    <text lang="eng">
      <p bold="true">Survival rule</p>
    </text>
  </region>
  <region id="59" left="18" top="1422" width="476" height="40" border="true" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Verwende niemals i als gewöhnliche Variable, wenn du mit 
komplexen Zahlen rechnest.</p>
    </text>
    <text lang="eng">
      <p>Survival rule: 
Never use i as ordinary variable if you handle complex numbers.</p>
    </text>
  </region>
  <region id="60" top="1467" color="#000000" bgColor="#ffffff">
    <area collapsed="true">
      <title lang="ger">
        <p>Begründung</p>
      </title>
      <title lang="eng">
        <p>Why?</p>
      </title>
    </area>
    <region id="61" left="18" top="1485" width="623" height="56" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="ger">
        <p>Es ist sehr einfach, die imaginäre Einheit versehentlich zu überschreiben, 
beispielsweise indem man i als Schleifenzähler verwendet. Dadurch werden 
komplexe Zahlen  eventuell nicht mehr richtig angezeigt.</p>
      </text>
      <text lang="eng">
        <p>It is very easy to unintendedly overwrite i, e.g. by use as loop counter.
Depending on optimization settings this may lead to incorrect display of complex 
numbers.</p>
      </text>
    </region>
    <region id="62" left="153" top="1548" width="135" height="58" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <description active="true" position="Top" lang="ger">
          <p>Optimierung&gt; Symbolisch</p>
        </description>
        <description active="true" position="Top" lang="eng">
          <p>Optimization&gt; Symbolic</p>
        </description>
        <input>
          <e type="operand">z.4</e>
          <e type="operand">3</e>
          <e type="operand" style="unit">m</e>
          <e type="operator" args="2">*</e>
          <e type="operand">e</e>
          <e type="operand">1</e>
          <e type="operator" args="1">-</e>
          <e type="function" preserve="true" args="1">sqrt</e>
          <e type="operand">π</e>
          <e type="operand">3</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region id="63" left="360" top="1548" width="135" height="58" color="#000000" bgColor="#ffffff" fontSize="10">
      <math optimize="2">
        <description active="true" position="Top" lang="ger">
          <p>Optimierung&gt; Numerisch</p>
        </description>
        <description active="true" position="Top" lang="eng">
          <p>Optimization&gt; Numeric</p>
        </description>
        <input>
          <e type="operand">z.5</e>
          <e type="operand">3</e>
          <e type="operand" style="unit">m</e>
          <e type="operator" args="2">*</e>
          <e type="operand">e</e>
          <e type="operand">1</e>
          <e type="operator" args="1">-</e>
          <e type="function" preserve="true" args="1">sqrt</e>
          <e type="operand">π</e>
          <e type="operand">3</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region id="64" left="162" top="1620" width="151" height="91" color="#000000" bgColor="#ffffff">
      <picture>
        <raw format="png" encoding="base64"> </raw>
      </picture>
    </region>
    <region id="65" left="360" top="1620" width="276" height="69" color="#000000" bgColor="#ffffff">
      <picture>
        <raw format="png" encoding="base64"> </raw>
      </picture>
    </region>
    <region id="66" left="18" top="1719" width="43" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">i</e>
          <e type="operand">0</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region id="67" left="153" top="1719" width="178" height="33" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">z.4</e>
        </input>
        <result action="numeric">
          <e type="operand">1.5</e>
          <e type="operand">2.5981</e>
          <e type="operand">i</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">+</e>
          <e type="bracket">(</e>
          <e type="operand" style="unit">m</e>
          <e type="operator" args="2">*</e>
        </result>
      </math>
    </region>
    <region id="68" left="360" top="1719" width="93" height="32" color="#ff0000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">z.5</e>
        </input>
        <result action="numeric">
          <e type="operand">1.5</e>
          <e type="operand" style="unit">m</e>
          <e type="operator" args="2">*</e>
        </result>
      </math>
    </region>
    <region id="69" left="486" top="1737" width="70" height="24" color="#ff0000" bgColor="#ffffff" fontSize="10">
      <text lang="ger">
        <p bold="true">Falsch!</p>
      </text>
      <text lang="eng">
        <p bold="true">Wrong!</p>
      </text>
    </region>
    <region id="70" left="18" top="1755" width="43" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">i</e>
          <e type="operand">1</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region id="71" left="153" top="1755" width="178" height="33" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">z.4</e>
        </input>
        <result action="numeric">
          <e type="operand">1.5</e>
          <e type="operand">2.5981</e>
          <e type="operand">i</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">+</e>
          <e type="bracket">(</e>
          <e type="operand" style="unit">m</e>
          <e type="operator" args="2">*</e>
        </result>
      </math>
    </region>
    <region id="72" left="360" top="1755" width="117" height="32" color="#ff0000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">z.5</e>
        </input>
        <result action="numeric">
          <e type="operand">4.0981</e>
          <e type="operand" style="unit">m</e>
          <e type="operator" args="2">*</e>
        </result>
      </math>
    </region>
    <region id="73" left="18" top="1791" width="66" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">i</e>
          <e type="operand">1</e>
          <e type="operator" args="1">-</e>
          <e type="function" preserve="true" args="1">sqrt</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region id="74" left="153" top="1791" width="178" height="33" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">z.4</e>
        </input>
        <result action="numeric">
          <e type="operand">1.5</e>
          <e type="operand">2.5981</e>
          <e type="operand">i</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">+</e>
          <e type="bracket">(</e>
          <e type="operand" style="unit">m</e>
          <e type="operator" args="2">*</e>
        </result>
      </math>
    </region>
    <region id="75" left="360" top="1791" width="178" height="33" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">z.5</e>
        </input>
        <result action="numeric">
          <e type="operand">1.5</e>
          <e type="operand">2.5981</e>
          <e type="operand">i</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">+</e>
          <e type="bracket">(</e>
          <e type="operand" style="unit">m</e>
          <e type="operator" args="2">*</e>
        </result>
      </math>
    </region>
    <region id="76" top="1818" color="#000000" bgColor="#ffffff">
      <area terminator="true" />
    </region>
  </region>
  <region id="77" left="18" top="1854" width="94" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Mathematik.sm">Mathematik</p>
    </text>
    <text lang="eng">
      <p href="Mathematik.sm">Mathematics</p>
    </text>
  </region>
  <region id="78" left="18" top="1872" width="61" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Handbook.sm">Inhalt</p>
    </text>
    <text lang="eng">
      <p href="Handbook.sm">Contents</p>
    </text>
  </region>
  <region id="79" left="18" top="1917" width="450" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p italic="true">$Author: mkraska $
$Date: 2013-09-29 02:42:17 +0200 (So, 29. Sep 2013) $ </p>
    </text>
  </region>
</regions>