// Numbas version: finer_feedback_settings
{"name": "Complex Numbers 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["ans1", "ans2", "ans3", "ans4", "b4", "b1", "b2", "b3", "d4", "d2", "s8", "s3", "s2", "s1", "s7", "s6", "s5", "s4", "z2", "tol", "c4", "a1", "a3", "a2", "a4", "z4", "z5", "z6", "z1", "c2", "z3", "f", "n"], "name": "Complex Numbers 1", "tags": [], "preamble": {"css": "", "js": ""}, "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|$</p>\n  <p>a) \\[ \\begin{eqnarray*} |\\var{z1}|&amp;=&amp;\\sqrt{(\\var{a1})^2+(\\var{b1})^2}\\\\ &amp;=&amp; \\var{abs(z1)}\\\\ &amp;=&amp;\\var{ans1} \\end{eqnarray*} \\] to 3 decimal places.</p>\n  <p>b) \\[ \\begin{eqnarray*} |(\\var{z2})(\\var{z3})|&amp;=&amp;|\\var{z2}|\\;|\\var{z3}|\\\\ &amp;=&amp; \\var{abs(z2)}\\times \\var{abs(z3)}\\\\ &amp;=&amp;\\var{abs(z2*z3)}\\\\ &amp;=&amp;\\var{ans2} \\end{eqnarray*} \\] to 3 decimal places.</p>\n  <p>c) \\[ \\begin{eqnarray*} |(\\var{z4})^{\\var{n}}|&amp;=&amp;|\\var{z4}|^{\\var{n}}\\\\ &amp;=&amp; \\var{abs(z4)}^{\\var{n}}\\\\ &amp;=&amp; \\var{abs(z4)^n}\\\\ &amp;=&amp;\\var{ans3} \\end{eqnarray*} \\] to 3 decimal places.</p>\n  <p>d) \\[ \\begin{eqnarray*} \\left|\\frac{\\var{z5}}{\\var{z6}}\\right|&amp;=&amp;\\frac{|\\var{z5}|}{|\\var{z6}|}\\\\ &amp;=&amp; \\frac{\\var{abs(z5)}}{\\var{abs(z6)}}\\\\ &amp;=&amp; \\var{abs(z5/z6)}\\\\ &amp;=&amp;\\var{ans4} \\end{eqnarray*} \\] to 3 decimal places.</p>", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "parts": [{"prompt": "<p>$|\\var{z1}|=\\;\\;$[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "ans1+tol", "minValue": "ans1-tol", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$|(\\var{z2})(\\var{z3})|=\\;\\;$[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "ans2+tol", "minValue": "ans2-tol", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$|(\\var{z4})^{\\var{n}}|=\\;\\;$[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "ans3+tol", "minValue": "ans3-tol", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>Let \\[z=\\frac{\\var{z5}}{\\var{z6}}\\]<br/>$|z|=\\;\\;$[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "ans4+tol", "minValue": "ans4-tol", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<p>Find the modulus of each of the following complex numbers, leaving your answer in decimal form to 3 decimal places:</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"ans1": {"definition": "precround(abs(z1),3)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans1", "description": ""}, "ans2": {"definition": "precround(abs(z2*z3),3)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans2", "description": ""}, "ans3": {"definition": "precround(abs(z4)^n,3)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans3", "description": ""}, "ans4": {"definition": "precround(abs(z5/z6),3)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans4", "description": ""}, "b4": {"definition": "s1*random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "b4", "description": ""}, "b1": {"definition": "s2*random(3..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "b1", "description": ""}, "b2": {"definition": "s5*random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "b2", "description": ""}, "b3": {"definition": "s1*random(1..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "b3", "description": ""}, "d4": {"definition": "s5*random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "d4", "description": ""}, "d2": {"definition": "s7*random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "d2", "description": ""}, "s8": {"definition": "random(1,-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "s8", "description": ""}, "s3": {"definition": "random(1,-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "s3", "description": ""}, "s2": {"definition": "random(1,-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "s2", "description": ""}, "s1": {"definition": "random(1,-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "s1", "description": ""}, "s7": {"definition": "random(1,-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "s7", "description": ""}, "s6": {"definition": "random(1,-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "s6", "description": ""}, "s5": {"definition": "random(1,-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "s5", "description": ""}, "s4": {"definition": "random(1,-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "s4", "description": ""}, "tol": {"definition": "0.001", "templateType": "anything", "group": "Ungrouped variables", "name": "tol", "description": ""}, "z3": {"definition": "c2+d2*i", "templateType": "anything", "group": "Ungrouped variables", "name": "z3", "description": ""}, "a1": {"definition": "s1*random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "a3": {"definition": "s3*random(1..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "a3", "description": ""}, "a2": {"definition": "s4*random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a2", "description": ""}, "a4": {"definition": "s8*random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a4", "description": ""}, "z4": {"definition": "a3+b3*i", "templateType": "anything", "group": "Ungrouped variables", "name": "z4", "description": ""}, "z5": {"definition": "a4+b4*i", "templateType": "anything", "group": "Ungrouped variables", "name": "z5", "description": ""}, "z6": {"definition": "c4+d4*i", "templateType": "anything", "group": "Ungrouped variables", "name": "z6", "description": ""}, "z1": {"definition": "a1+b1*i", "templateType": "anything", "group": "Ungrouped variables", "name": "z1", "description": ""}, "z2": {"definition": "a2+b2*i", "templateType": "anything", "group": "Ungrouped variables", "name": "z2", "description": ""}, "c4": {"definition": "if(a4=f,f+1,f)", "templateType": "anything", "group": "Ungrouped variables", "name": "c4", "description": ""}, "f": {"definition": "random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "n": {"definition": "random(3..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "n", "description": ""}, "c2": {"definition": "s6*random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "c2", "description": ""}}, "metadata": {"description": "<p>Finding the modulus of four complex numbers; includes finding the modulus of a product, a power and a quotient. By Newcastle University</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Mark Hodds", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/510/"}]}]}], "contributors": [{"name": "Mark Hodds", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/510/"}]}