<?xml version="1.0" encoding="UTF-8"?>
<quiz>
  <question type="stack">
    <name>
      <text>Complex_Convert_2</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p>Consider the complex number \(z\) with modulus \(|z| = {@absz@}\) and argument \(\arg(z) = {@argz@} \).</p>
<p>Convert this number into the form \(p + qi\) where \(p\) and \(q\) are real.</p>
<p>[[input:ans1]] [[validation:ans1]]</p>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p> To convert the complex number \(z\) with modulus \(|z| = {@absz@}\) and argument \(\arg(z) = {@argz@} \) into the form \(p + qi\) where \(p\) and \(q\) are real we use trigonometry.</p>
<p>\[p=r \cos(\theta)={@absz@}\cdot \cos({@argz@})={@pval@}\ ,\] and, \[q=r \sin(\theta)={@absz@}\cdot \sin({@argz@})={@qval@}\]</p>
<p>Hence the answer is \({@z1@}\)</p>]]></text>
    </generalfeedback>
    <defaultgrade>1</defaultgrade>
    <penalty>0</penalty>
    <hidden>0</hidden>
    <idnumber/>
    <stackversion>
      <text>2018080600</text>
    </stackversion>
    <questionvariables>
      <text>fr:rand([1/6,1/3,1/4,1/2,3/4,2/3]);
argz:((-1)^rand(2))*Pi*fr;
absz:rand(5)+2;

pval:ev(absz*cos(argz));
qval:ev(absz*sin(argz));

z1:ev(pval + qval * i, simp);
zreal:ev(realpart(z1),simp);
zimag:ev(imagpart(z1),simp);</text>
    </questionvariables>
    <specificfeedback format="html">
      <text><![CDATA[<p>[[feedback:Result]]</p>]]></text>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>\(|z| = {@absz@}\) and argument \(\arg(z) = {@argz@} \) gives {@z1@}.</text>
    </questionnote>
    <questiondescription format="moodle_auto_format">
      <text/>
    </questiondescription>
    <questionsimplify>1</questionsimplify>
    <assumepositive>0</assumepositive>
    <assumereal>0</assumereal>
    <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>
    <logicsymbol>lang</logicsymbol>
    <matrixparens>[</matrixparens>
    <isbroken>0</isbroken>
    <variantsselectionseed/>
    <input>
      <name>ans1</name>
      <type>algebraic</type>
      <tans>z1</tans>
      <boxsize>20</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint/>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords>sin,cos</forbidwords>
      <allowwords/>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>1</requirelowestterms>
      <checkanswertype>1</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options/>
    </input>
    <prt>
      <name>Result</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackstyle>1</feedbackstyle>
      <feedbackvariables>
        <text>sansr:ev(realpart(ans1),simp);
sansi:ev(imagpart(ans1),simp);</text>
      </feedbackvariables>
      <node>
        <name>0</name>
        <description/>
        <answertest>EqualComAss</answertest>
        <sans>ans1</sans>
        <tans>z1</tans>
        <testoptions/>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty/>
        <truenextnode>-1</truenextnode>
        <trueanswernote>Result-0-T </trueanswernote>
        <truefeedback format="html">
          <text/>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty/>
        <falsenextnode>3</falsenextnode>
        <falseanswernote>Result-0-F </falseanswernote>
        <falsefeedback format="html">
          <text/>
        </falsefeedback>
      </node>
      <node>
        <name>1</name>
        <description/>
        <answertest>AlgEquiv</answertest>
        <sans>sansr</sans>
        <tans>zreal</tans>
        <testoptions/>
        <quiet>0</quiet>
        <truescoremode>+</truescoremode>
        <truescore>0.3300000</truescore>
        <truepenalty/>
        <truenextnode>2</truenextnode>
        <trueanswernote>Result-1-T </trueanswernote>
        <truefeedback format="html">
          <text><![CDATA[<p>The real part of your answer is correct.</p>]]></text>
        </truefeedback>
        <falsescoremode>+</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty/>
        <falsenextnode>2</falsenextnode>
        <falseanswernote>Result-1-F </falseanswernote>
        <falsefeedback format="html">
          <text><![CDATA[<p>The real part of your answer is incorrect</p>]]></text>
        </falsefeedback>
      </node>
      <node>
        <name>2</name>
        <description/>
        <answertest>AlgEquiv</answertest>
        <sans>sansi</sans>
        <tans>zimag</tans>
        <testoptions/>
        <quiet>0</quiet>
        <truescoremode>+</truescoremode>
        <truescore>0.3300000</truescore>
        <truepenalty/>
        <truenextnode>-1</truenextnode>
        <trueanswernote>Result-2-T </trueanswernote>
        <truefeedback format="html">
          <text><![CDATA[<p>The imaginary part of your answer is correct.</p>]]></text>
        </truefeedback>
        <falsescoremode>+</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty/>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>Result-2-F </falseanswernote>
        <falsefeedback format="html">
          <text><![CDATA[<p>The imaginary part of your answer is incorrect.</p>]]></text>
        </falsefeedback>
      </node>
      <node>
        <name>3</name>
        <description/>
        <answertest>AlgEquiv</answertest>
        <sans>ans1</sans>
        <tans>z1</tans>
        <testoptions/>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>0.2000000</truescore>
        <truepenalty/>
        <truenextnode>-1</truenextnode>
        <trueanswernote>Result-3-T </trueanswernote>
        <truefeedback format="html">
          <text><![CDATA[<p>Your answer is equivalent to the correct answer, but not in the required format \(p + q i\).</p>]]></text>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty/>
        <falsenextnode>1</falsenextnode>
        <falseanswernote>Result-3-F </falseanswernote>
        <falsefeedback format="html">
          <text/>
        </falsefeedback>
      </node>
    </prt>
    <deployedseed>955968713</deployedseed>
    <deployedseed>74643407</deployedseed>
    <deployedseed>1095844454</deployedseed>
    <deployedseed>841826427</deployedseed>
    <deployedseed>1896493661</deployedseed>
    <deployedseed>921663555</deployedseed>
    <deployedseed>1000092521</deployedseed>
    <deployedseed>1681383876</deployedseed>
    <deployedseed>1176553749</deployedseed>
    <deployedseed>1855636254</deployedseed>
    <deployedseed>314736758</deployedseed>
    <deployedseed>1642903931</deployedseed>
    <deployedseed>1666831870</deployedseed>
    <deployedseed>1316951705</deployedseed>
    <deployedseed>1485602074</deployedseed>
    <deployedseed>1104229356</deployedseed>
    <deployedseed>316121015</deployedseed>
    <qtest>
      <testcase>1</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>z1</value>
      </testinput>
      <expected>
        <name>Result</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>Result-0-T</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>2</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>ev(z1+1,simp)</value>
      </testinput>
      <expected>
        <name>Result</name>
        <expectedscore>0.3300000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>Result-2-T</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>3</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>ev(z1+i,simp)</value>
      </testinput>
      <expected>
        <name>Result</name>
        <expectedscore>0.3300000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>Result-2-F</expectedanswernote>
      </expected>
    </qtest>
  </question>
</quiz>
