// Numbas version: exam_results_page_options
{"name": "The distance between two 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)", "description": "", "name": "s1"}, "tol": {"templateType": "anything", "group": "Ungrouped variables", "definition": "0.001", "description": "", "name": "tol"}, "b3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "if(d2=t2,t2+random(1..4),t2)", "description": "", "name": "b3"}, "s5": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "name": "s5"}, "t2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "s5*random(1..9)", "description": "", "name": "t2"}, 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"anything", "group": "Ungrouped variables", "definition": "s1*random(1..9)", "description": "", "name": "a3"}, "a4": {"templateType": "anything", "group": "Ungrouped variables", "definition": "s6*random(1..9)", "description": "", "name": "a4"}, "s3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "name": "s3"}, "s6": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "name": "s6"}, "s7": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "name": "s7"}}, "ungrouped_variables": ["ans1", "ans2", "ans3", "b4", "b1", "b2", "b3", "d4", "d2", "s3", "s2", "s1", "s7", "s6", "s5", "s4", "z2", "tol", "z3", "a1", "a3", "a2", "a4", "z4", "z5", "z6", "z1", "c2", "c4", "t2", "t3", "t1"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "The distance between two complex numbers", "showQuestionGroupNames": false, "functions": {}, "parts": [{"showCorrectAnswer": true, "scripts": {}, "gaps": [{"correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "allowFractions": false, "type": "numberentry", "maxValue": "ans1+tol", "minValue": "ans1-tol", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "showPrecisionHint": false}], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "prompt": "\n      \n      \n      <p>Find the distance between $\\var{z1}$ and $\\var{z2}$.</p>\n      \n      \n      \n      <p>Distance = [[0]]</p>\n      \n      \n      ", "variableReplacements": [], "marks": 0}, {"showCorrectAnswer": true, "scripts": {}, "gaps": [{"correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "allowFractions": false, "type": "numberentry", "maxValue": "ans2+tol", "minValue": "ans2-tol", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "showPrecisionHint": false}], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "prompt": "\n      \n      \n      <p>Find the distance between $\\var{z3}$ and $\\var{z4}$.</p>\n      \n      \n      \n      <p>Distance = [[0]]</p>\n      \n      \n      ", "variableReplacements": [], "marks": 0}, {"showCorrectAnswer": true, "scripts": {}, "gaps": [{"correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "allowFractions": false, "type": "numberentry", "maxValue": "ans3+tol", "minValue": "ans3-tol", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "showPrecisionHint": false}], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "prompt": "\n      \n      \n      <p>Find the distance between $\\var{z5}$ and $\\var{z6}$.</p>\n      \n      \n      \n      <p>Distance = [[0]]</p>\n      \n      \n      ", "variableReplacements": [], "marks": 0}], "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "<p>Find the distance between the following complex numbers, leaving your answer in decimal form to 3 decimal places:</p>", "tags": ["checked2015", "complex numbers", "distance between complex numbers", "mas1602", "MAS1602", "modulus", "modulus of a complex number", "modulus of complex numbers"], "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "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>Perhaps more steps are needed in the solutions? It isn't explained how to find the modulus of the complex number.&nbsp;<strong>Explanation included in Advice.</strong></p>\n<p>Question appears to be working correctly.</p>\n<p><strong>13/07/2012:</strong></p>\n<p>Set new variable tol=0 for all numeric input.</p>", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Finding the distance between two complex numbers using the modulus of their difference. Three parts.</p>"}, "advice": "\n  \n  \n  <p>The distance D between two complex numbers $z_1=a+bi$ and $z_2=c+di$ is given by the modulus of the difference i.e.<br/>\\[D=|z_1-z_2| = |(a-c)+(b-d)i|=\\sqrt{(a-c)^2+(b-d)^2}\\]<br/>Applying to the questions we have:\t\t\t\t\t<br/>a) \\[ \\begin{eqnarray*} D&#38;=&#38;|(\\var{z1})-(\\var{z2})|\\\\\n  \n  &#38;=&#38;|\\var{z1-z2}|\\\\\n  \n  &#38;=&#38; \\var{abs(z1-z2)}\\\\\n  \n  &#38;=&#38;\\var{ans1}\n  \n  \\end{eqnarray*} \\] to 3 decimal places.</p>\n  \n  \n  \n  <p>b) \\[ \\begin{eqnarray*} D&#38;=&#38;|(\\var{z3})-(\\var{z4})|\\\\\n  \n  &#38;=&#38;|\\var{z3-z4}|\\\\\n  \n  &#38;=&#38; \\var{abs(z3-z4)}\\\\\n  \n  &#38;=&#38;\\var{ans2}\n  \n  \\end{eqnarray*} \\] to 3 decimal places.</p>\n  \n  \n  \n  <p>c) \\[ \\begin{eqnarray*} D&#38;=&#38;|(\\var{z5})-(\\var{z6})|\\\\\n  \n  &#38;=&#38;|\\var{z5-z6}|\\\\\n  \n  &#38;=&#38; \\var{abs(z5-z6)}\\\\\n  \n  &#38;=&#38;\\var{ans3}\n  \n  \\end{eqnarray*} \\] to 3 decimal places.</p>\n  \n  \n  ", "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/"}]}