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