<?xml version="1.0" encoding="UTF-8"?>
<quiz>
  <question type="multichoice">
    <name>
      <text>10.2.3.7 Modulus</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p class="HELM_exercise">Exercise</p>
<p>Which of the following are true?</p>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>Let \(z = r(\cos \theta + i\sin \theta)\). Then \(|z| = r \implies |z|^2 = r^2\). Also we have \(z^2 = r^2 (\cos \theta + i\sin \theta)^2\) which implies that \(|z^2| = r^2\). Therefore \( |z^2| = |z|^2 \).</p><p><br></p>

<p>Let \(z = a + ib\). Then \(zz^* = (a+ib)(a-ib) = a^2 + b^2\). Note that \(|z| = \sqrt{a^2 + b^2}\) which implies that \(|z|^2 = a^2+b^2\). Therefore \( z z^* = |z|^2 \).</p>]]></text>
    </generalfeedback>
    <defaultgrade>1</defaultgrade>
    <penalty>0.3333333</penalty>
    <hidden>0</hidden>
    <idnumber/>
    <single>false</single>
    <shuffleanswers>true</shuffleanswers>
    <answernumbering>none</answernumbering>
    <showstandardinstruction>1</showstandardinstruction>
    <correctfeedback format="html">
      <text>Your answer is correct.</text>
    </correctfeedback>
    <partiallycorrectfeedback format="html">
      <text>Your answer is partially correct.</text>
    </partiallycorrectfeedback>
    <incorrectfeedback format="html">
      <text>Your answer is incorrect.</text>
    </incorrectfeedback>
    <shownumcorrect/>
    <answer fraction="50" format="html">
      <text><![CDATA[<p>\( |z^2| = |z|^2 \)</p>]]></text>
      <feedback format="html">
        <text/>
      </feedback>
    </answer>
    <answer fraction="50" format="html">
      <text><![CDATA[<p>\( z z^* = |z|^2 \)</p>]]></text>
      <feedback format="html">
        <text/>
      </feedback>
    </answer>
    <answer fraction="0" format="html">
      <text><![CDATA[<p>\( z z^* = z^2 \)</p>]]></text>
      <feedback format="html">
        <text/>
      </feedback>
    </answer>
    <answer fraction="0" format="html">
      <text><![CDATA[<p>\( z z^* = |z| \)</p>]]></text>
      <feedback format="html">
        <text/>
      </feedback>
    </answer>
    <answer fraction="0" format="html">
      <text><![CDATA[<p>\( |z^2| = z^2 \)</p>]]></text>
      <feedback format="html">
        <text/>
      </feedback>
    </answer>
  </question>
</quiz>
