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<quiz>
  <question type="stack">
    <name>
      <text>10.1.2.17 Algebra of complex numbers (NOT IN QUIZ)</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p class="HELM_exercise">Exercise </p>
<ol class="HELM_parts">
    <p>If <span class="math inline">\(z={@exp1@}\)</span>, <span class="math inline">\(w={@exp2@}\)</span> find expressions (in standard Cartesian form) for</p>

    <li>
        <p>\(z-3w=\) [[input:ans1]] [[validation:ans1]] [[feedback:prt1]]</p>
    </li>

    <li>
        <p>\(zw^*=\) [[input:ans2]] [[validation:ans2]] [[feedback:prt2]]</p>
    </li>

    <li>
        <p>\( \displaystyle{\left(\frac{z}{w}\right)^* = }\) [[input:ans3]] [[validation:ans3]] [[feedback:prt3]]</p>
    </li>

    <li>
        <p>\(\displaystyle{\left\vert\frac{z}{w}\right\vert= }\) [[input:ans4]] [[validation:ans4]] [[feedback:prt4]]</p>
    </li>

</ol>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<ol class="HELM_parts">
    <p>If&nbsp;<span>\(z={@exp1@}\)</span>,&nbsp;<span>\(w={@exp2@}\),&nbsp;</span></p>
    <li>
        <p><span>\(z-3w=({@exp1@})-3*({@exp2@})={@ta1@}\).</span><br></p>
    </li>
    <li>
        <p><span>\(zw^*=({@exp1@})({@exp2@})^*={@ta2@}\).<br></span></p>
    </li>
    <li>
        <p><span>\(\left(\dfrac{z}{w}\right)^*=\left(\dfrac{@exp1@}{@exp2@}\right)^*=\displaystyle{{@ta3@}}\).&nbsp;</span></p>
    </li>
    <li>
        <p><span>\( \left\vert \dfrac{z}{w}\right\vert= \left\vert \dfrac{@exp1@}{@exp2@} \right\vert=\displaystyle{{@ta4@}}\).<br></span></p>
    </li>
</ol>]]></text>
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      <text>2020120600</text>
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    <questionvariables>
      <text>n1: 1+rand(5);
n2: 2+rand(5);
n3: 1+rand(4);
n4: 2+rand(4);
exp1: simplify(n1+%i*n2);
exp2: n3+%i*n4;
ta1: ev((n1-3*n3)+(n2-3*n4)*%i,simp);
ta2: ev(expand(exp1*(n3-%i*n4)),simp);
ta3:((n1*n3+n2*n4)-%i*(n2*n3-n1*n4))/(n3^2+n4^2);
ta4: sqrt((n1*n3+n2*n4)^2+(n2*n3-n1*n4)^2)/(n3^2+n4^2);
wta3: ((n1*n3+n2*n4)+%i*(n2*n3-n1*n4))/(n3^2+n4^2);</text>
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    <questionnote format="moodle_auto_format">
      <text>\(z={@exp1@}\), \(w={@exp2@}\), \(z-3w={@ta1@}\), \(zw^*={@ta2@}\), \( \displaystyle{\left(\frac{z}{w}\right)^* = {@ta3@}}\), \(\displaystyle{\lvert\frac{z}{w}\rvert={@ta4@} }\)</text>
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      <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Correct answer, well done.]]></text>
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      <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Your answer is partially correct.]]></text>
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    <prtincorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Incorrect answer.]]></text>
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