// Numbas version: finer_feedback_settings
{"name": "The modulus of complex numbers", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "variables": {"s1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1,-1)", "name": "s1", "description": ""}, "tol": {"templateType": "anything", "group": "Ungrouped variables", "definition": "0.001", "name": "tol", "description": ""}, "b3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "s1*random(1..4)", "name": "b3", "description": ""}, "s5": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1,-1)", "name": "s5", "description": ""}, "c4": {"templateType": "anything", "group": "Ungrouped variables", "definition": "if(a4=f,f+1,f)", "name": "c4", "description": ""}, "b4": {"templateType": "anything", "group": "Ungrouped variables", "definition": "s1*random(1..9)", "name": "b4", "description": ""}, "s4": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1,-1)", "name": "s4", "description": ""}, "s2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1,-1)", "name": "s2", "description": ""}, "a1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "s1*random(2..9)", "name": "a1", "description": ""}, "z5": {"templateType": "anything", "group": "Ungrouped variables", "definition": "a4+b4*i", "name": "z5", "description": ""}, "c2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "s6*random(1..9)", "name": "c2", "description": ""}, "d2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "s7*random(1..9)", "name": "d2", "description": ""}, "n": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(3..5)", 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"fractionNumbers", "!noLeadingMinus"]}, "name": "The modulus of complex numbers", "functions": {}, "showQuestionGroupNames": false, "parts": [{"showCorrectAnswer": true, "scripts": {}, "gaps": [{"showCorrectAnswer": true, "showPrecisionHint": false, "allowFractions": false, "scripts": {}, "type": "numberentry", "correctAnswerFraction": false, "minValue": "ans1-tol", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "maxValue": "ans1+tol"}], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "prompt": "<p>$|\\var{z1}|=\\;\\;$[[0]]</p>", "variableReplacements": [], "marks": 0}, {"showCorrectAnswer": true, "scripts": {}, "gaps": [{"showCorrectAnswer": true, "showPrecisionHint": false, "allowFractions": false, "scripts": {}, "type": "numberentry", "correctAnswerFraction": false, "minValue": "ans2-tol", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "maxValue": "ans2+tol"}], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "prompt": "<p>$|(\\var{z2})(\\var{z3})|=\\;\\;$[[0]]</p>", "variableReplacements": [], "marks": 0}, {"showCorrectAnswer": true, "scripts": {}, "gaps": [{"showCorrectAnswer": true, "showPrecisionHint": false, "allowFractions": false, "scripts": {}, "type": "numberentry", "correctAnswerFraction": false, "minValue": "ans3-tol", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "maxValue": "ans3+tol"}], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "prompt": "<p>$|(\\var{z4})^{\\var{n}}|=\\;\\;$[[0]]</p>", "variableReplacements": [], "marks": 0}, {"showCorrectAnswer": true, "scripts": {}, "gaps": [{"showCorrectAnswer": true, "showPrecisionHint": false, "allowFractions": false, "scripts": {}, "type": "numberentry", "correctAnswerFraction": false, "minValue": "ans4-tol", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "maxValue": "ans4+tol"}], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "prompt": "<p>Let \\[z=\\frac{\\var{z5}}{\\var{z6}}\\]<br/>$|z|=\\;\\;$[[0]]</p>", "variableReplacements": [], "marks": 0}], "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "<p>Find the modulus of each of the following complex numbers, leaving your answer in decimal form to 3 decimal places:</p>", "tags": ["checked2015", "complex number", "complex numbers", "division of complex numbers", "mas1602", "MAS1602", "modulus of a complex number", "modulus of complex numbers", "modulus of the division of complex numbers", "modulus of the power of complex numbers", "modulus of the product of complex numbers", "multiplication of complex numbers", "multiply complex numbers", "product of complex numbers", "properties of the modulus of complex numbers", "rationalise the denominator", "rationalising the denominator"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "<p><strong>15/07/2015:</strong></p>\n<p>Added tags.</p>\n<p><strong>5/07/2012:</strong></p>\n<p>Added tags.</p>\n<p>Question appears to be working correctly. &nbsp;</p>", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Finding the modulus of four complex numbers; includes finding the modulus of a product, a power and a quotient.</p>"}, "advice": "<p>Recall that $|a+bi|=\\sqrt{a^2+b^2}$ and that:</p>\n  <p>1. $ |z^n| = |z|^n$</p>\n  <p>2. $ |z_1z_2|=|z_1|\\;|z_2|$</p>\n  <p>3. $ |z_1/z_2|=|z_1|/|z_2|$</p>\n  <p>a) \\[ \\begin{eqnarray*} |\\var{z1}|&amp;=&amp;\\sqrt{(\\var{a1})^2+(\\var{b1})^2}\\\\ &amp;=&amp; \\var{abs(z1)}\\\\ &amp;=&amp;\\var{ans1} \\end{eqnarray*} \\] to 3 decimal places.</p>\n  <p>b) \\[ \\begin{eqnarray*} |(\\var{z2})(\\var{z3})|&amp;=&amp;|\\var{z2}|\\;|\\var{z3}|\\\\ &amp;=&amp; \\var{abs(z2)}\\times \\var{abs(z3)}\\\\ &amp;=&amp;\\var{abs(z2*z3)}\\\\ &amp;=&amp;\\var{ans2} \\end{eqnarray*} \\] to 3 decimal places.</p>\n  <p>c) \\[ \\begin{eqnarray*} |(\\var{z4})^{\\var{n}}|&amp;=&amp;|\\var{z4}|^{\\var{n}}\\\\ &amp;=&amp; \\var{abs(z4)}^{\\var{n}}\\\\ &amp;=&amp; \\var{abs(z4)^n}\\\\ &amp;=&amp;\\var{ans3} \\end{eqnarray*} \\] to 3 decimal places.</p>\n  <p>d) \\[ \\begin{eqnarray*} \\left|\\frac{\\var{z5}}{\\var{z6}}\\right|&amp;=&amp;\\frac{|\\var{z5}|}{|\\var{z6}|}\\\\ &amp;=&amp; \\frac{\\var{abs(z5)}}{\\var{abs(z6)}}\\\\ &amp;=&amp; \\var{abs(z5/z6)}\\\\ &amp;=&amp;\\var{ans4} \\end{eqnarray*} \\] to 3 decimal places.</p>", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}