<?xml version="1.0" encoding="UTF-8"?>
<quiz>
  <question type="stack">
    <name>
      <text>Complex_Convert_1</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p>Consider the complex number \[z={@z1@} \] Evaluate the modulus of \(z\) \((r = |z|)\) and the principal value of the argument of \(z\) (\(\theta = \mathrm{Arg}(z)\)). Enter your results in the correct order, i.e. \([r,\theta]\).</p>
<p> </p>
<p>\([r,\theta] = \) [[input:ans1]] [[validation:ans1]]</p>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>\[r=\sqrt{x^2+y^2}\] \[r=\sqrt{\left({@x@}\right)^2+\left({@y@}\right)^2}=\sqrt{{@x*x@}+{@y*y@}}\] \[r=\sqrt{@x*x+y*y@}={@rval@}\] \[tan(\mathrm{arg}(z))=\frac{y}{x}=\frac{@y@}{@x@}={@y/x@}\] \[\mathrm{arg}(z)={@argsol@} + k\cdot\pi\] Considering the appropriate quadrant of the complex plane to fix \(k\), we find that \[\mathrm{arg}(z)={@principaltheta@}\].</p>]]></text>
    </generalfeedback>
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      <text/>
    </stackversion>
    <questionvariables>
      <text>argset:[Pi/6,Pi/4,Pi/3];
 n1:rand(3)+1;
 modsol:rand(5)+1;
 argsol:ev(((-1)^rand(2))*(rand(2)*Pi-argset[n1]),simp);
 z1:ev(modsol*cos(argsol) + modsol*i*sin(argsol),simp);
 x:modsol*cos(argsol);
 y:modsol*sin(argsol);
 rval:sqrt(x*x+y*y);
 principaltheta:%pi - mod (%pi - argsol, 2*%pi);</text>
    </questionvariables>
    <specificfeedback format="html">
      <text><![CDATA[<p>[[feedback:Result]]</p>]]></text>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>\(z={@z1@}\)  gives \([{@modsol@},{@principaltheta@}]\)</text>
    </questionnote>
    <questiondescription format="moodle_auto_format">
      <text/>
    </questiondescription>
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    <prtcorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Correct answer, well done.]]></text>
    </prtcorrect>
    <prtpartiallycorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Your answer is partially correct.]]></text>
    </prtpartiallycorrect>
    <prtincorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Incorrect answer.]]></text>
    </prtincorrect>
    <decimals>.</decimals>
    <scientificnotation>*10</scientificnotation>
    <multiplicationsign>dot</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
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      <name>ans1</name>
      <type>algebraic</type>
      <tans>[modsol,principaltheta]</tans>
      <boxsize>20</boxsize>
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      <name>Result</name>
      <value>2.0000000</value>
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        <answertest>AlgEquiv</answertest>
        <sans>ans1</sans>
        <tans>[modsol,principaltheta]</tans>
        <testoptions/>
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        <trueanswernote>Result-0-T </trueanswernote>
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          <text/>
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        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
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        <falseanswernote>Result-0-F </falseanswernote>
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    <qtest>
      <testcase>1</testcase>
      <description/>
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        <name>ans1</name>
        <value>[modsol,principaltheta]</value>
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        <value>[x,y]</value>
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        <name>Result</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>Result-0-F</expectedanswernote>
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  </question>
</quiz>
