// Numbas version: exam_results_page_options
{"name": "Rectangular to Polar Conversion - Radians", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Practice to decide which quadrant a complex number lies in.</p>"}, "tags": [], "name": "Rectangular to Polar Conversion - Radians", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "ungrouped_variables": ["b1", "q1", "q3", "q2", "q4", "s2", "s1", "quad", "a1", "z1", "t", "rez", "imz", "modz", "argz", "tol"], "statement": "", "extensions": [], "parts": [{"gaps": [{"precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "precision": "2", "showPrecisionHint": true, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "strictPrecision": false, "precisionType": "dp", "marks": 1, "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain", "minValue": "modz-tol", "scripts": {}, "allowFractions": false, "correctAnswerFraction": false, "maxValue": "modz+tol", "showFeedbackIcon": true}, {"precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "precision": "2", "showPrecisionHint": true, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "strictPrecision": false, "precisionType": "dp", "marks": 1, "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain", "minValue": "argz-tol", "scripts": {}, "allowFractions": false, "correctAnswerFraction": false, "maxValue": "argz+tol", "showFeedbackIcon": true}], "prompt": "<p>Find the modulus and argument (in radians) of the complex number $z=\\var{z1}$.</p>\n<p>$|z| = $ [[0]]</p>\n<p>$\\arg(z) = $ [[1]] radians.</p>", "type": "gapfill", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "showCorrectAnswer": true, "scripts": {}, "marks": 0, "variableReplacements": []}], "advice": "<p>Firstly, $|z| = \\sqrt{(\\var{a1})^2+(\\var{b1})^2} = \\sqrt{\\var{a1*a1+b1*b1}} = \\var{dpformat(modz,2)}$</p>\n<p>Secondly, since the real part of $z$ is {rez} and the imaginary part of $z$ is {imz}, {quad} So,</p>\n<p>$\\arg(z) = \\var{dpformat(argz,2)}$ radians.</p>\n<p><br/>&nbsp;</p>", "preamble": {"css": "", "js": ""}, "variable_groups": [], "variables": {"q3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "'The complex number is in the third quadrant.'", "name": "q3", "description": ""}, "t": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..4)", "name": "t", "description": ""}, "imz": {"templateType": "anything", "group": "Ungrouped variables", "definition": "if (b1>=0,\"Positive\",\"Negative\")", "name": "imz", "description": "<p>im</p>"}, "s1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "switch(t=1,1,t=4,1,-1)", "name": "s1", "description": ""}, "b1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "s2*random(1..10)", "name": "b1", "description": ""}, "z1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "a1+b1*i", "name": "z1", "description": ""}, "quad": {"templateType": "anything", "group": "Ungrouped variables", "definition": "switch(t=1,q1,t=2,q2,t=3,q3,q4)", "name": "quad", "description": ""}, "argz": {"templateType": "anything", "group": "Ungrouped variables", "definition": "if(arg(z1)<0,arg(z1)+2*pi,arg(z1))", "name": "argz", "description": ""}, "q1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "'The complex number is in the first quadrant.'", "name": "q1", "description": ""}, "q4": {"templateType": "anything", "group": "Ungrouped variables", "definition": "'The complex number is in the fourth quadrant.'", "name": "q4", "description": ""}, "modz": {"templateType": "anything", "group": "Ungrouped variables", "definition": "abs(z1)", "name": "modz", "description": ""}, "rez": {"templateType": "anything", "group": "Ungrouped variables", "definition": "if (a1>=0,\"Positive\",\"Negative\")", "name": "rez", "description": ""}, "q2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "'The complex number is in the second quadrant.'", "name": "q2", "description": ""}, "tol": {"templateType": "anything", "group": "Ungrouped variables", "definition": "0.01", "name": "tol", "description": ""}, "s2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "switch(t=4,-1,t=3,-1,1)", "name": "s2", "description": ""}, "a1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "s1*random(1..10)", "name": "a1", "description": ""}}, "functions": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "type": "question", "contributors": [{"name": "Peter Johnston", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/771/"}]}]}], "contributors": [{"name": "Peter Johnston", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/771/"}]}