// Numbas version: finer_feedback_settings
{"name": "Luis's copy of 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": [{"question_groups": [{"name": "", "pickingStrategy": "all-ordered", "questions": [], "pickQuestions": 0}], "statement": "<p>Find the distance between the following complex numbers, leaving your answer in decimal form to 3 decimal places:</p>", "variablesTest": {"maxRuns": 100, "condition": ""}, "tags": ["checked2015", "complex numbers", "distance between complex numbers", "mas1602", "MAS1602", "modulus", "modulus of a complex number", "modulus of complex numbers"], "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>", "description": "<p>Finding the distance between two complex numbers using the modulus of their difference. Three parts.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "parts": [{"variableReplacements": [], "gaps": [{"variableReplacements": [], "minValue": "ans1-tol", "maxValue": "ans1+tol", "allowFractions": false, "marks": 1, "type": "numberentry", "showCorrectAnswer": true, "scripts": {}, "showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false}], "marks": 0, "type": "gapfill", "showCorrectAnswer": true, "scripts": {}, "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      ", "variableReplacementStrategy": "originalfirst"}, {"variableReplacements": [], "gaps": [{"variableReplacements": [], "minValue": "ans2-tol", "maxValue": "ans2+tol", "allowFractions": false, "marks": 1, "type": "numberentry", "showCorrectAnswer": true, "scripts": {}, "showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false}], "marks": 0, "type": "gapfill", "showCorrectAnswer": true, "scripts": {}, "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      ", "variableReplacementStrategy": "originalfirst"}, {"variableReplacements": [], "gaps": [{"variableReplacements": [], "minValue": "ans3-tol", "maxValue": "ans3+tol", "allowFractions": false, "marks": 1, "type": "numberentry", "showCorrectAnswer": true, "scripts": {}, "showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false}], "marks": 0, "type": "gapfill", "showCorrectAnswer": true, "scripts": {}, "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      ", "variableReplacementStrategy": "originalfirst"}], "variables": {"z2": {"name": "z2", "definition": "a2+b2*i", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "s1": {"name": "s1", "definition": "random(1,-1)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "t2": {"name": "t2", "definition": "s5*random(1..9)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "ans3": {"name": "ans3", "definition": "precround(abs(z5-z6),3)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "s7": {"name": "s7", "definition": "random(1,-1)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "a1": {"name": "a1", "definition": "s1*random(1..9)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "a2": {"name": "a2", "definition": "s2*random(1..9)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "z5": {"name": "z5", "definition": "a4+b4*i", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "t3": {"name": "t3", "definition": "s7*random(1..9)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "a3": {"name": "a3", "definition": "s1*random(1..9)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "s5": {"name": "s5", "definition": "random(1,-1)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "c4": {"name": "c4", "definition": "s4*random(1..9)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "b3": {"name": "b3", "definition": "if(d2=t2,t2+random(1..4),t2)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "z4": {"name": "z4", "definition": "a3+b3*i", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "z1": {"name": "z1", "definition": "a1+b1*i", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "b1": {"name": "b1", "definition": "if(b2=t1,t1+random(1..4),t1)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "a4": {"name": "a4", "definition": "s6*random(1..9)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "ans1": {"name": "ans1", "definition": "precround(abs(z1-z2),3)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "s6": {"name": "s6", "definition": "random(1,-1)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "c2": {"name": "c2", "definition": "s6*random(1..9)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "t1": {"name": "t1", "definition": "s4*random(1..9)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "tol": {"name": "tol", "definition": "0.001", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "z6": {"name": "z6", "definition": "c4+d4*i", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "d4": {"name": "d4", "definition": "if(b4=t3,t3+random(1..4),t3)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "s4": {"name": "s4", "definition": "random(1,-1)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "ans2": {"name": "ans2", "definition": "precround(abs(z3-z4),3)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "d2": {"name": "d2", "definition": "s7*random(1..9)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "s3": {"name": "s3", "definition": "random(1,-1)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "b2": {"name": "b2", "definition": "s5*random(1..9)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "s2": {"name": "s2", "definition": "random(1,-1)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "z3": {"name": "z3", "definition": "c2+d2*i", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "b4": {"name": "b4", "definition": "s1*random(1..9)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}}, "name": "Luis's copy of The distance between two complex numbers", "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  ", "preamble": {"js": "", "css": ""}, "showQuestionGroupNames": false, "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"], "type": "question", "functions": {}, "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "variable_groups": [], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Luis Hernandez", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2870/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Luis Hernandez", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2870/"}]}