// Numbas version: finer_feedback_settings
{"name": "01 - Complex Numbers | Exercises", "metadata": {"description": "<p>Self-assessment questions. Solve 50% of the available marks to pass this exercise.</p>", "licence": "Creative Commons Attribution-ShareAlike 4.0 International"}, "duration": 0, "percentPass": "50", "showQuestionGroupNames": false, "showstudentname": true, "question_groups": [{"name": "Participants of B1 lecture", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", ""], "questions": [{"name": "W01Q02", "extensions": ["geogebra"], "custom_part_types": [], "resources": [["question-resources/solution1.PNG", "/srv/numbas/media/question-resources/solution1.PNG"], ["question-resources/solution2.PNG", "/srv/numbas/media/question-resources/solution2.PNG"], ["question-resources/solution3.PNG", "/srv/numbas/media/question-resources/solution3.PNG"], ["question-resources/solution4.PNG", "/srv/numbas/media/question-resources/solution4.PNG"], ["question-resources/solution2.1.PNG", "/srv/numbas/media/question-resources/solution2.1.PNG"], ["question-resources/solution2.2.PNG", "/srv/numbas/media/question-resources/solution2.2.PNG"], ["question-resources/solution2.3.PNG", "/srv/numbas/media/question-resources/solution2.3.PNG"], ["question-resources/solution2.4.PNG", "/srv/numbas/media/question-resources/solution2.4.PNG"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "seb SEE", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1836/"}, {"name": "Philipp Bucher", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2658/"}], "variables": {}, "advice": "<h2><strong>Solution for the exercises above:</strong></h2>\n<p><strong><img src=\"resources/question-resources/solution2.1.PNG\" width=\"409\" height=\"471\"/><img src=\"resources/question-resources/solution2.2.PNG\" width=\"482\" height=\"413\"/></strong></p>\n<p><strong><img src=\"resources/question-resources/solution2.3.PNG\" width=\"536\" height=\"320\"/><img src=\"resources/question-resources/solution2.4.PNG\" width=\"398\" height=\"459\"/></strong></p>", "parts": [{"gaps": [{"marks": 1, "valuegenerators": [], "customName": "vi-a", "type": "jme", "useCustomName": true, "checkVariableNames": false, "showCorrectAnswer": false, "variableReplacementStrategy": "originalfirst", "vsetRange": [0, 1], "checkingAccuracy": 0.001, "showPreview": true, "checkingType": "absdiff", "customMarkingAlgorithm": "", "vsetRangePoints": 5, "failureRate": 1, "scripts": {}, "extendBaseMarkingAlgorithm": true, "adaptiveMarkingPenalty": 0, "unitTests": [], "answer": "1/2", "variableReplacements": [], "showFeedbackIcon": true}, {"marks": 1, "valuegenerators": [], "customName": "vi-b", "type": "jme", "useCustomName": true, "checkVariableNames": false, "showCorrectAnswer": false, "variableReplacementStrategy": "originalfirst", "vsetRange": [0, 1], "checkingAccuracy": 0.001, "showPreview": true, "checkingType": "absdiff", "customMarkingAlgorithm": "", "vsetRangePoints": 5, "failureRate": 1, "scripts": {}, "extendBaseMarkingAlgorithm": true, "adaptiveMarkingPenalty": 0, "unitTests": [], "answer": "1/2", "variableReplacements": [], "showFeedbackIcon": true}, {"marks": 1, "valuegenerators": [], "customName": "G1", "type": "jme", "useCustomName": true, "checkVariableNames": false, "showCorrectAnswer": false, "variableReplacementStrategy": "originalfirst", "vsetRange": [0, 1], "checkingAccuracy": 0.001, "showPreview": true, "checkingType": "absdiff", "customMarkingAlgorithm": "", "vsetRangePoints": 5, "failureRate": 1, "scripts": {}, "extendBaseMarkingAlgorithm": true, "adaptiveMarkingPenalty": 0, "unitTests": [], "answer": "-1/2", "variableReplacements": [], "showFeedbackIcon": true}, {"marks": 1, "valuegenerators": [], "customName": "G2", "type": "jme", "useCustomName": true, "checkVariableNames": false, "showCorrectAnswer": false, "variableReplacementStrategy": "originalfirst", "vsetRange": [0, 1], "checkingAccuracy": 0.001, "showPreview": true, "checkingType": "absdiff", "customMarkingAlgorithm": "", "vsetRangePoints": 5, "failureRate": 1, "scripts": {}, "extendBaseMarkingAlgorithm": true, "adaptiveMarkingPenalty": 0, "unitTests": [], "answer": "-1/2", "variableReplacements": [], "showFeedbackIcon": true}, {"marks": 1, "valuegenerators": [], "customName": "G3", "type": "jme", "useCustomName": true, "checkVariableNames": false, "showCorrectAnswer": false, "variableReplacementStrategy": "originalfirst", "vsetRange": [0, 1], "checkingAccuracy": 0.001, "showPreview": true, "checkingType": "absdiff", "customMarkingAlgorithm": "", "vsetRangePoints": 5, "failureRate": 1, "scripts": {}, "extendBaseMarkingAlgorithm": true, "adaptiveMarkingPenalty": 0, "unitTests": [], "answer": "1/2*sqrt(2)", "variableReplacements": [], "showFeedbackIcon": true}, {"marks": 1, "valuegenerators": [], "customName": "G4", "type": "jme", "useCustomName": true, "checkVariableNames": false, "showCorrectAnswer": false, "variableReplacementStrategy": "originalfirst", "vsetRange": [0, 1], "checkingAccuracy": 0.001, "showPreview": true, "checkingType": "absdiff", "customMarkingAlgorithm": "", "vsetRangePoints": 5, "failureRate": 1, "scripts": {}, "extendBaseMarkingAlgorithm": true, "adaptiveMarkingPenalty": 0, "unitTests": [], "answer": "5/4", "variableReplacements": [], "showFeedbackIcon": true}, {"marks": 1, "valuegenerators": [], "customName": "G5", "type": "jme", "useCustomName": true, "checkVariableNames": false, "showCorrectAnswer": false, "variableReplacementStrategy": "originalfirst", "vsetRange": [0, 1], "checkingAccuracy": 0.001, "showPreview": true, "checkingType": "absdiff", "customMarkingAlgorithm": "", "vsetRangePoints": 5, "failureRate": 1, "scripts": {}, "extendBaseMarkingAlgorithm": true, "adaptiveMarkingPenalty": 0, "unitTests": [], "answer": "-1/2+i*1/2", "variableReplacements": [], "showFeedbackIcon": true}], "marks": 0, "scripts": {}, "customName": "(a)", "extendBaseMarkingAlgorithm": true, "adaptiveMarkingPenalty": 0, "useCustomName": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "prompt": "<p><strong>$z = \\dfrac{1}{i-1}$</strong></p>\n<p style=\"text-align: right;\">$z= $ [[2]]$+i $ [[3]]&nbsp;</p>\n<p style=\"text-align: right;\">$z=$[[4]]$\\exp(i$[[5]]$\\pi)$</p>\n<p></p>", "unitTests": [], "type": "gapfill", "sortAnswers": false, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "showFeedbackIcon": true}, {"gaps": [{"marks": 1, "valuegenerators": [], "customName": "G1", "type": "jme", "useCustomName": true, "checkVariableNames": false, "showCorrectAnswer": false, "variableReplacementStrategy": "originalfirst", "vsetRange": [0, 1], "checkingAccuracy": 0.001, "showPreview": true, "checkingType": "absdiff", "customMarkingAlgorithm": "", "vsetRangePoints": 5, "failureRate": 1, "scripts": {}, "extendBaseMarkingAlgorithm": true, "adaptiveMarkingPenalty": 0, "unitTests": [], "answer": "0", "variableReplacements": [], "showFeedbackIcon": true}, {"marks": 1, "valuegenerators": [], "customName": "G2", "type": "jme", "useCustomName": true, "checkVariableNames": false, "showCorrectAnswer": false, "variableReplacementStrategy": "originalfirst", "vsetRange": [0, 1], "checkingAccuracy": 0.001, "showPreview": true, "checkingType": "absdiff", "customMarkingAlgorithm": "", "vsetRangePoints": 5, "failureRate": 1, "scripts": {}, "extendBaseMarkingAlgorithm": true, "adaptiveMarkingPenalty": 0, "unitTests": [], "answer": "2", "variableReplacements": [], "showFeedbackIcon": true}, {"marks": 1, "valuegenerators": [], "customName": "G3", "type": "jme", "useCustomName": true, "checkVariableNames": false, "showCorrectAnswer": false, "variableReplacementStrategy": "originalfirst", "vsetRange": [0, 1], "checkingAccuracy": 0.001, "showPreview": true, "checkingType": "absdiff", "customMarkingAlgorithm": "", "vsetRangePoints": 5, "failureRate": 1, "scripts": {}, "extendBaseMarkingAlgorithm": true, "adaptiveMarkingPenalty": 0, "unitTests": [], "answer": "2", "variableReplacements": [], "showFeedbackIcon": true}, {"marks": 1, "valuegenerators": [], "customName": "G4", "type": "jme", "useCustomName": true, "checkVariableNames": false, "showCorrectAnswer": false, "variableReplacementStrategy": "originalfirst", "vsetRange": [0, 1], "checkingAccuracy": 0.001, "showPreview": true, "checkingType": "absdiff", "customMarkingAlgorithm": "", "vsetRangePoints": 5, "failureRate": 1, "scripts": {}, "extendBaseMarkingAlgorithm": true, "adaptiveMarkingPenalty": 0, "unitTests": [], "answer": "1/2", "variableReplacements": [], "showFeedbackIcon": true}], "marks": 0, "scripts": {}, "customName": "(b)", "extendBaseMarkingAlgorithm": true, "adaptiveMarkingPenalty": 0, "useCustomName": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "prompt": "<p><strong>$z = i^2+2i+1$.</strong></p>\n<p style=\"text-align: right;\">$z= $[[0]]$+i $[[1]]&nbsp;&nbsp;</p>\n<p style=\"text-align: right;\">$z=$ [[2]]$\\exp(i$[[3]]$\\pi)$</p>\n<p></p>", "unitTests": [], "type": "gapfill", "sortAnswers": false, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "showFeedbackIcon": true}, {"gaps": [{"marks": 1, "valuegenerators": [], "customName": "G1", "type": "jme", "useCustomName": true, "checkVariableNames": false, "showCorrectAnswer": false, "variableReplacementStrategy": "originalfirst", "vsetRange": [0, 1], "checkingAccuracy": 0.001, "showPreview": true, "checkingType": "absdiff", "customMarkingAlgorithm": "", "vsetRangePoints": 5, "failureRate": 1, "scripts": {}, "extendBaseMarkingAlgorithm": true, "adaptiveMarkingPenalty": 0, "unitTests": [], "answer": "-1", "variableReplacements": [], "showFeedbackIcon": true}, {"marks": 1, "valuegenerators": [], "customName": "G2", "type": "jme", "useCustomName": true, "checkVariableNames": false, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "vsetRange": [0, 1], "checkingAccuracy": 0.001, "showPreview": true, "checkingType": "absdiff", "customMarkingAlgorithm": "", "vsetRangePoints": 5, "failureRate": 1, "scripts": {}, "extendBaseMarkingAlgorithm": true, "adaptiveMarkingPenalty": 0, "unitTests": [], "answer": "0", "variableReplacements": [], "showFeedbackIcon": true}, {"marks": 1, "valuegenerators": [], "customName": "G3", "type": "jme", "useCustomName": true, "checkVariableNames": false, "showCorrectAnswer": false, "variableReplacementStrategy": "originalfirst", "vsetRange": [0, 1], "checkingAccuracy": 0.001, "showPreview": true, "checkingType": "absdiff", "customMarkingAlgorithm": "", "vsetRangePoints": 5, "failureRate": 1, "scripts": {}, "extendBaseMarkingAlgorithm": true, "adaptiveMarkingPenalty": 0, "unitTests": [], "answer": "1", "variableReplacements": [], "showFeedbackIcon": true}, {"marks": 1, "valuegenerators": [], "customName": "G4", "type": "jme", "useCustomName": true, "checkVariableNames": false, "showCorrectAnswer": false, "variableReplacementStrategy": "originalfirst", "vsetRange": [0, 1], "checkingAccuracy": 0.001, "showPreview": true, "checkingType": "absdiff", "customMarkingAlgorithm": "", "vsetRangePoints": 5, "failureRate": 1, "scripts": {}, "extendBaseMarkingAlgorithm": true, "adaptiveMarkingPenalty": 0, "unitTests": [], "answer": "1", "variableReplacements": [], "showFeedbackIcon": true}], "marks": 0, "scripts": {}, "customName": "(c)", "extendBaseMarkingAlgorithm": true, "adaptiveMarkingPenalty": 0, "useCustomName": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "prompt": "<p><strong>$z = \\left(\\dfrac{1+i}{1-i}\\right)^2$</strong></p>\n<p style=\"text-align: right;\">$z= $[[0]]$+i $[[1]] &nbsp;</p>\n<p style=\"text-align: right;\">$z=$ [[2]]$\\exp(\\pm i$[[3]]$\\pi)$</p>\n<p style=\"text-align: right;\"></p>", "unitTests": [], "type": "gapfill", "sortAnswers": false, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "showFeedbackIcon": true}, {"gaps": [{"marks": 1, "valuegenerators": [], "customName": "G1", "type": "jme", "useCustomName": true, "checkVariableNames": false, "showCorrectAnswer": false, "variableReplacementStrategy": "originalfirst", "vsetRange": [0, 1], "checkingAccuracy": 0.001, "showPreview": true, "checkingType": "absdiff", "customMarkingAlgorithm": "", "vsetRangePoints": 5, "failureRate": 1, "scripts": {}, "extendBaseMarkingAlgorithm": true, "adaptiveMarkingPenalty": 0, "unitTests": [], "answer": "-25/17", "variableReplacements": [], "showFeedbackIcon": true}, {"marks": 1, "valuegenerators": [], "customName": "G2", "type": "jme", "useCustomName": true, "checkVariableNames": false, "showCorrectAnswer": false, "variableReplacementStrategy": "originalfirst", "vsetRange": [0, 1], "checkingAccuracy": 0.001, "showPreview": true, "checkingType": "absdiff", "customMarkingAlgorithm": "", "vsetRangePoints": 5, "failureRate": 1, "scripts": {}, "extendBaseMarkingAlgorithm": true, "adaptiveMarkingPenalty": 0, "unitTests": [], "answer": "19/17", "variableReplacements": [], "showFeedbackIcon": true}, {"marks": 1, "valuegenerators": [], "customName": "G3", "type": "jme", "useCustomName": true, "checkVariableNames": false, "showCorrectAnswer": false, "variableReplacementStrategy": "originalfirst", "vsetRange": [0, 1], "checkingAccuracy": "0.01", "showPreview": true, "checkingType": "absdiff", "customMarkingAlgorithm": "", "vsetRangePoints": 5, "failureRate": 1, "scripts": {}, "extendBaseMarkingAlgorithm": true, "adaptiveMarkingPenalty": 0, "unitTests": [], "answer": "sqrt(58/17)", "variableReplacements": [], "showFeedbackIcon": true}, {"marks": 1, "valuegenerators": [], "customName": "G4", "type": "jme", "useCustomName": true, "checkVariableNames": false, "showCorrectAnswer": false, "variableReplacementStrategy": "originalfirst", "vsetRange": [0, 1], "checkingAccuracy": 0.001, "showPreview": true, "checkingType": "absdiff", "customMarkingAlgorithm": "", "vsetRangePoints": 5, "failureRate": 1, "scripts": {}, "extendBaseMarkingAlgorithm": true, "adaptiveMarkingPenalty": 0, "unitTests": [], "answer": "0.79", "variableReplacements": [], "showFeedbackIcon": true}], "marks": 0, "scripts": {}, "customName": "(d)", "extendBaseMarkingAlgorithm": true, "adaptiveMarkingPenalty": 0, "useCustomName": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "prompt": "<p><strong>$z = \\dfrac{3i-7}{i+4}$</strong></p>\n<p style=\"text-align: right;\">$z= $[[0]]$+i $[[1]]</p>\n<p style=\"text-align: right;\">$z=$ [[2]]$\\exp(i0.79\\pi)$</p>", "unitTests": [], "type": "gapfill", "sortAnswers": false, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "showFeedbackIcon": true}, {"gaps": [{"marks": 1, "valuegenerators": [], "customName": "G1", "type": "jme", "useCustomName": true, "checkVariableNames": false, "showCorrectAnswer": false, "variableReplacementStrategy": "originalfirst", "vsetRange": [0, 1], "checkingAccuracy": "0.01", "showPreview": true, "checkingType": "absdiff", "customMarkingAlgorithm": "", "vsetRangePoints": 5, "failureRate": 1, "scripts": {}, "extendBaseMarkingAlgorithm": true, "adaptiveMarkingPenalty": 0, "unitTests": [], "answer": "cos(-1.1)*2.8", "variableReplacements": [], "showFeedbackIcon": true}, {"marks": 1, "valuegenerators": [], "customName": "G2", "type": "jme", "useCustomName": true, "checkVariableNames": false, "showCorrectAnswer": false, "variableReplacementStrategy": "originalfirst", "vsetRange": [0, 1], "checkingAccuracy": "0.01", "showPreview": true, "checkingType": "absdiff", "customMarkingAlgorithm": "", "vsetRangePoints": 5, "failureRate": 1, "scripts": {}, "extendBaseMarkingAlgorithm": true, "adaptiveMarkingPenalty": 0, "unitTests": [], "answer": "sin(-1.1)*2.8", "variableReplacements": [], "showFeedbackIcon": true}, {"marks": 1, "valuegenerators": [], "customName": "G3", "type": "jme", "useCustomName": true, "checkVariableNames": false, "showCorrectAnswer": false, "variableReplacementStrategy": "originalfirst", "vsetRange": [0, 1], "checkingAccuracy": 0.001, "showPreview": true, "checkingType": "absdiff", "customMarkingAlgorithm": "", "vsetRangePoints": 5, "failureRate": 1, "scripts": {}, "extendBaseMarkingAlgorithm": true, "adaptiveMarkingPenalty": 0, "unitTests": [], "answer": "2.8", "variableReplacements": [], "showFeedbackIcon": true}, {"marks": 1, "valuegenerators": [], "customName": "G4", "type": "jme", "useCustomName": true, "checkVariableNames": false, "showCorrectAnswer": false, "variableReplacementStrategy": "originalfirst", "vsetRange": [0, 1], "checkingAccuracy": "0.01", "showPreview": true, "checkingType": "absdiff", "customMarkingAlgorithm": "", "vsetRangePoints": 5, "failureRate": 1, "scripts": {}, "extendBaseMarkingAlgorithm": true, "adaptiveMarkingPenalty": 0, "unitTests": [], "answer": "1.1/pi", "variableReplacements": [], "showFeedbackIcon": true}], "marks": 0, "scripts": {}, "customName": "(e)", "extendBaseMarkingAlgorithm": true, "adaptiveMarkingPenalty": 0, "useCustomName": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "prompt": "<p><strong>$z = 2.8e^{-i1.1}$</strong></p>\n<p style=\"text-align: right;\">$z= $[[0]]$+i ($[[1]]$)$</p>\n<p style=\"text-align: right;\">$z=$ [[2]]$\\exp(-i$[[3]]$\\pi)$</p>\n<p></p>\n<p></p>\n<p></p>", "unitTests": [], "type": "gapfill", "sortAnswers": false, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "showFeedbackIcon": true}], "rulesets": {}, "metadata": {"description": "<p>First question of exercise 1</p>", "licence": "None specified"}, "ungrouped_variables": [], "functions": {}, "preamble": {"css": "", "js": ""}, "variablesTest": {"condition": "", "maxRuns": 100}, "variable_groups": [], "statement": "<h2><strong>W01Q02</strong></h2>\n<hr/>\n<p>Simplify each complex number to the form $x+iy$ and $|z|e^{i\\mathrm{Arg}(z)}$.</p>", "tags": [], "type": "question"}, {"name": "W01Q03", "extensions": ["geogebra"], "custom_part_types": [], "resources": [["question-resources/solution1.PNG", "/srv/numbas/media/question-resources/solution1.PNG"], ["question-resources/solution2.PNG", "/srv/numbas/media/question-resources/solution2.PNG"], ["question-resources/solution3.PNG", "/srv/numbas/media/question-resources/solution3.PNG"], ["question-resources/solution4.PNG", "/srv/numbas/media/question-resources/solution4.PNG"], ["question-resources/solution2.1.PNG", "/srv/numbas/media/question-resources/solution2.1.PNG"], ["question-resources/solution2.2.PNG", "/srv/numbas/media/question-resources/solution2.2.PNG"], ["question-resources/solution2.3.PNG", "/srv/numbas/media/question-resources/solution2.3.PNG"], ["question-resources/solution2.4.PNG", "/srv/numbas/media/question-resources/solution2.4.PNG"], ["question-resources/solution3.1.PNG", "/srv/numbas/media/question-resources/solution3.1.PNG"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "seb SEE", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1836/"}, {"name": "Philipp Bucher", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2658/"}], "variables": {"a": {"description": "", "templateType": "anything", "name": "a", "group": "Ungrouped variables", "definition": "vector(1,1)"}, "defs": {"description": "", "templateType": "anything", "name": "defs", "group": "Ungrouped variables", "definition": "[\n  ['z',a]\n  ]"}}, "advice": "<h2><strong>Solution for the exercises above:</strong></h2>\n<p><strong><img src=\"resources/question-resources/solution3.1.PNG\" width=\"429\" height=\"244\"/></strong></p>", "parts": [{"gaps": [{"marks": 1, "valuegenerators": [], "customName": "G1", "type": "jme", "useCustomName": true, "checkVariableNames": false, "showCorrectAnswer": false, "variableReplacementStrategy": "originalfirst", "vsetRange": [0, 1], "checkingAccuracy": 0.001, "notallowed": {"partialCredit": 0, "message": "Please don't copy the task!", "strings": ["abs"], "showStrings": true}, "showPreview": true, "checkingType": "absdiff", "customMarkingAlgorithm": "", "vsetRangePoints": 5, "failureRate": 1, "scripts": {}, "extendBaseMarkingAlgorithm": true, "adaptiveMarkingPenalty": 0, "unitTests": [], "answer": "1", "variableReplacements": [], "showFeedbackIcon": true}], "marks": 0, "scripts": {}, "customName": "(a)", "extendBaseMarkingAlgorithm": true, "adaptiveMarkingPenalty": 0, "useCustomName": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "prompt": "<p><strong>$z = \\dfrac{2i-1}{i-2}$</strong></p>\n<p style=\"text-align: right;\"><br/>$\\vert{}z \\vert{} =$[[0]]</p>\n<p></p>", "unitTests": [], "type": "gapfill", "sortAnswers": false, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "showFeedbackIcon": true}, {"gaps": [{"marks": 1, "valuegenerators": [], "customName": "G1", "type": "jme", "useCustomName": true, "checkVariableNames": false, "showCorrectAnswer": false, "variableReplacementStrategy": "originalfirst", "vsetRange": [0, 1], "checkingAccuracy": 0.001, "notallowed": {"partialCredit": 0, "message": "Please don't copy the task!", "strings": ["abs"], "showStrings": true}, "showPreview": true, "checkingType": "absdiff", "customMarkingAlgorithm": "", "vsetRangePoints": 5, "failureRate": 1, "scripts": {}, "extendBaseMarkingAlgorithm": true, "adaptiveMarkingPenalty": 0, "unitTests": [], "answer": "13^2", "variableReplacements": [], "showFeedbackIcon": true}], "marks": 0, "scripts": {}, "customName": "(b)", "extendBaseMarkingAlgorithm": true, "adaptiveMarkingPenalty": 0, "useCustomName": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "prompt": "<p><strong>$z = (2-3i)^4$</strong></p>\n<p style=\"text-align: right;\">$\\vert{}z \\vert{} =$[[0]]</p>\n<p></p>", "unitTests": [], "type": "gapfill", "sortAnswers": false, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "showFeedbackIcon": true}], "rulesets": {}, "metadata": {"description": "<p>First question of exercise 1</p>", "licence": "None specified"}, "ungrouped_variables": ["defs", "a"], "functions": {}, "preamble": {"css": "", "js": ""}, "variablesTest": {"condition": "", "maxRuns": 100}, "variable_groups": [], "statement": "<h2><strong>W01Q03</strong></h2>\n<hr/>\n<p>Find the absolute value of following complex numbers. Try using the relation $\\vert{}z \\vert{} = \\sqrt{ z \\bar{z} }$.</p>", "tags": [], "type": "question"}, {"name": "W01Q04", "extensions": ["geogebra"], "custom_part_types": [], "resources": [["question-resources/solution1.PNG", "/srv/numbas/media/question-resources/solution1.PNG"], ["question-resources/solution2.PNG", "/srv/numbas/media/question-resources/solution2.PNG"], ["question-resources/solution3.PNG", "/srv/numbas/media/question-resources/solution3.PNG"], ["question-resources/solution4.PNG", "/srv/numbas/media/question-resources/solution4.PNG"], ["question-resources/solution2.1.PNG", "/srv/numbas/media/question-resources/solution2.1.PNG"], ["question-resources/solution2.2.PNG", "/srv/numbas/media/question-resources/solution2.2.PNG"], ["question-resources/solution2.3.PNG", "/srv/numbas/media/question-resources/solution2.3.PNG"], ["question-resources/solution2.4.PNG", "/srv/numbas/media/question-resources/solution2.4.PNG"], ["question-resources/solution3.1.PNG", "/srv/numbas/media/question-resources/solution3.1.PNG"], ["question-resources/solution4.1.PNG", "/srv/numbas/media/question-resources/solution4.1.PNG"], ["question-resources/solution4.2.PNG", "/srv/numbas/media/question-resources/solution4.2.PNG"], ["question-resources/solution4.3.PNG", "/srv/numbas/media/question-resources/solution4.3.PNG"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "seb SEE", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1836/"}, {"name": "Philipp Bucher", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2658/"}], "parts": [{"showFeedbackIcon": true, "marks": 0, "useCustomName": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "gaps": [{"variableReplacements": [], "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "useCustomName": true, "extendBaseMarkingAlgorithm": true, "checkingAccuracy": 0.001, "vsetRangePoints": 5, "showPreview": true, "vsetRange": [0, 1], "marks": 1, "checkingType": "absdiff", "showCorrectAnswer": false, "failureRate": 1, "adaptiveMarkingPenalty": 0, "scripts": {}, "unitTests": [], "checkVariableNames": false, "customName": "G1", "customMarkingAlgorithm": "", "valuegenerators": [], "answer": "-1/2", "type": "jme"}, {"variableReplacements": [], "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "useCustomName": true, "extendBaseMarkingAlgorithm": true, "checkingAccuracy": 0.001, "vsetRangePoints": 5, "showPreview": true, "vsetRange": [0, 1], "marks": 1, "checkingType": "absdiff", "showCorrectAnswer": false, "failureRate": 1, "adaptiveMarkingPenalty": 0, "scripts": {}, "unitTests": [], "checkVariableNames": false, "customName": "G2", "customMarkingAlgorithm": "", "valuegenerators": [], "answer": "3", "type": "jme"}], "adaptiveMarkingPenalty": 0, "scripts": {}, "unitTests": [], "customName": "(a)", "sortAnswers": false, "customMarkingAlgorithm": "", "prompt": "<p><strong>$2ix+3 = y-1$</strong></p>\n<p style=\"text-align: right;\">$x =$[[0]]<br/>$y =$[[1]]</p>\n<p></p>", "variableReplacements": [], "showCorrectAnswer": true, "type": "gapfill"}, {"showFeedbackIcon": true, "marks": 0, "useCustomName": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "gaps": [{"variableReplacements": [], "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "useCustomName": true, "extendBaseMarkingAlgorithm": true, "checkingAccuracy": 0.001, "vsetRangePoints": 5, "showPreview": true, "vsetRange": [0, 1], "marks": "1", "checkingType": "absdiff", "showCorrectAnswer": false, "failureRate": 1, "adaptiveMarkingPenalty": 0, "scripts": {}, "unitTests": [], "checkVariableNames": false, "customName": "Gy", "customMarkingAlgorithm": "", "valuegenerators": [{"value": "", "name": "x"}], "answer": "x", "type": "jme"}, {"variableReplacements": [], "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "useCustomName": true, "extendBaseMarkingAlgorithm": true, "checkingAccuracy": 0.001, "vsetRangePoints": 5, "showPreview": true, "vsetRange": [0, 1], "marks": "1", "checkingType": "absdiff", "showCorrectAnswer": false, "failureRate": 1, "adaptiveMarkingPenalty": 0, "scripts": {}, "unitTests": [], "checkVariableNames": false, "customName": "Gx", "customMarkingAlgorithm": "", "valuegenerators": [{"value": "", "name": "y"}], "answer": "y", "type": "jme"}], "adaptiveMarkingPenalty": 0, "scripts": {}, "unitTests": [], "customName": "(b)", "sortAnswers": false, "customMarkingAlgorithm": "", "prompt": "<p><strong>$x+iy = y+ix$</strong></p>\n<p style=\"text-align: right;\">$x =$ [[1]]<br/>$y =$ [[0]]</p>\n<p></p>", "variableReplacements": [], "showCorrectAnswer": true, "type": "gapfill"}, {"showFeedbackIcon": true, "marks": 0, "useCustomName": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "gaps": [{"variableReplacements": [], "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "useCustomName": true, "extendBaseMarkingAlgorithm": true, "checkingAccuracy": "0.01", "vsetRangePoints": 5, "showPreview": true, "vsetRange": [0, 1], "marks": 1, "checkingType": "absdiff", "showCorrectAnswer": false, "failureRate": 1, "adaptiveMarkingPenalty": 0, "scripts": {}, "unitTests": [], "checkVariableNames": false, "customName": "Gx", "customMarkingAlgorithm": "", "valuegenerators": [], "answer": "-1/7", "type": "jme"}, {"variableReplacements": [], "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "useCustomName": true, "extendBaseMarkingAlgorithm": true, "checkingAccuracy": "0.01", "vsetRangePoints": 5, "showPreview": true, "vsetRange": [0, 1], "marks": 1, "checkingType": "absdiff", "showCorrectAnswer": false, "failureRate": 1, "adaptiveMarkingPenalty": 0, "scripts": {}, "unitTests": [], "checkVariableNames": false, "customName": "Gy", "customMarkingAlgorithm": "", "valuegenerators": [], "answer": "-10/7", "type": "jme"}], "adaptiveMarkingPenalty": 0, "scripts": {}, "unitTests": [], "customName": "(c)", "sortAnswers": false, "customMarkingAlgorithm": "", "prompt": "<p><strong>$(x+2y+3)+i(3x-y-1)=0$</strong></p>\n<p style=\"text-align: right;\">$x =$[[0]]<br/>$y =$[[1]]</p>\n<p></p>", "variableReplacements": [], "showCorrectAnswer": true, "type": "gapfill"}, {"showFeedbackIcon": true, "marks": 0, "useCustomName": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "gaps": [{"variableReplacements": [], "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "useCustomName": true, "extendBaseMarkingAlgorithm": true, "checkingAccuracy": 0.001, "vsetRangePoints": 5, "showPreview": true, "vsetRange": [0, 1], "marks": "1", "checkingType": "absdiff", "showCorrectAnswer": false, "failureRate": 1, "adaptiveMarkingPenalty": 0, "scripts": {}, "unitTests": [], "checkVariableNames": false, "customName": "Gy", "customMarkingAlgorithm": "", "valuegenerators": [{"value": "", "name": "x"}], "answer": "-x", "type": "jme"}, {"variableReplacements": [], "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "useCustomName": true, "extendBaseMarkingAlgorithm": true, "checkingAccuracy": 0.001, "vsetRangePoints": 5, "showPreview": true, "vsetRange": [0, 1], "marks": "1", "checkingType": "absdiff", "showCorrectAnswer": false, "failureRate": 1, "adaptiveMarkingPenalty": 0, "scripts": {}, "unitTests": [], "checkVariableNames": false, "customName": "Gx", "customMarkingAlgorithm": "", "valuegenerators": [{"value": "", "name": "y"}], "answer": "-y", "type": "jme"}], "adaptiveMarkingPenalty": 0, "scripts": {}, "unitTests": [], "customName": "(d)", "sortAnswers": false, "customMarkingAlgorithm": "", "prompt": "<p><strong>$\\dfrac{x+iy}{x-iy}=-i$</strong></p>\n<p style=\"text-align: right;\">$x =$[[1]]<br/>$y =$[[0]]</p>\n<p></p>", "variableReplacements": [], "showCorrectAnswer": true, "type": "gapfill"}], "variable_groups": [], "ungrouped_variables": ["defs", "a"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "<h2><strong>Solution for the exercises above:</strong></h2>\n<p><strong><img src=\"resources/question-resources/solution4.1.PNG\" width=\"421\" height=\"214\"/><img src=\"resources/question-resources/solution4.2.PNG\" width=\"423\" height=\"310\"/></strong></p>\n<p><strong><img src=\"resources/question-resources/solution4.3.PNG\" width=\"290\" height=\"159\"/></strong></p>", "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "<h2><strong>W01Q04</strong></h2>\n<hr/>\n<p>Solve for all possible values of the real numbers $x$ and $y$ the following equations.</p>", "rulesets": {}, "variables": {"a": {"templateType": "anything", "name": "a", "description": "", "definition": "vector(1,1)", "group": "Ungrouped variables"}, "defs": {"templateType": "anything", "name": "defs", "description": "", "definition": "[\n  ['z',a]\n  ]", "group": "Ungrouped variables"}}, "functions": {}, "metadata": {"licence": "None specified", "description": "<p>First question of exercise 1</p>"}, "type": "question"}, {"name": "W01Q05", "extensions": ["geogebra"], "custom_part_types": [], "resources": [["question-resources/solution1.PNG", "/srv/numbas/media/question-resources/solution1.PNG"], ["question-resources/solution2.PNG", "/srv/numbas/media/question-resources/solution2.PNG"], ["question-resources/solution3.PNG", "/srv/numbas/media/question-resources/solution3.PNG"], ["question-resources/solution4.PNG", "/srv/numbas/media/question-resources/solution4.PNG"], ["question-resources/solution2.1.PNG", "/srv/numbas/media/question-resources/solution2.1.PNG"], ["question-resources/solution2.2.PNG", "/srv/numbas/media/question-resources/solution2.2.PNG"], ["question-resources/solution2.3.PNG", "/srv/numbas/media/question-resources/solution2.3.PNG"], ["question-resources/solution2.4.PNG", "/srv/numbas/media/question-resources/solution2.4.PNG"], ["question-resources/solution3.1.PNG", "/srv/numbas/media/question-resources/solution3.1.PNG"], ["question-resources/solution4.1.PNG", "/srv/numbas/media/question-resources/solution4.1.PNG"], ["question-resources/solution4.2.PNG", "/srv/numbas/media/question-resources/solution4.2.PNG"], ["question-resources/solution4.3.PNG", "/srv/numbas/media/question-resources/solution4.3.PNG"], ["question-resources/solution5.1.PNG", "/srv/numbas/media/question-resources/solution5.1.PNG"], ["question-resources/solution5.2.PNG", "/srv/numbas/media/question-resources/solution5.2.PNG"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "seb SEE", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1836/"}, {"name": "Philipp Bucher", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2658/"}], "parts": [{"adaptiveMarkingPenalty": 0, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "type": "gapfill", "scripts": {}, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "customName": "(a)", "unitTests": [], "useCustomName": true, "prompt": "<p><strong>$\\vert{}z-1\\vert{}=1$&nbsp;</strong>with $z=x+iy$.</p>\n<p>In the complex plane this equation describes a [[0]]</p>", "gaps": [{"customMarkingAlgorithm": "", "customName": "G1", "unitTests": [], "marks": 0, "displayColumns": 0, "displayType": "radiogroup", "matrix": ["1", 0, 0], "adaptiveMarkingPenalty": 0, "maxMarks": 0, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "shuffleChoices": false, "type": "1_n_2", "showCellAnswerState": true, "scripts": {}, "showFeedbackIcon": true, "distractors": ["", "", ""], "showCorrectAnswer": true, "useCustomName": true, "extendBaseMarkingAlgorithm": true, "choices": ["circle", "hyperbola", "line"], "minMarks": 0}], "marks": 0, "variableReplacements": [], "sortAnswers": false}, {"adaptiveMarkingPenalty": 0, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "type": "gapfill", "scripts": {}, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "customName": "(b)", "unitTests": [], "useCustomName": true, "prompt": "<p><strong>$\\mathrm{Re}(z^2)=4$&nbsp;</strong>with $z=x+iy$</p>\n<p>In the complex plane this equation describes a [[0]]</p>\n<p></p>", "gaps": [{"customMarkingAlgorithm": "", "customName": "G1", "unitTests": [], "marks": 0, "displayColumns": 0, "displayType": "radiogroup", "matrix": [0, "1", 0], "adaptiveMarkingPenalty": 0, "maxMarks": 0, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "shuffleChoices": false, "type": "1_n_2", "showCellAnswerState": true, "scripts": {}, "showFeedbackIcon": true, "distractors": ["", "", ""], "showCorrectAnswer": true, "useCustomName": true, 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"", "js": ""}, "variable_groups": [], "ungrouped_variables": ["defs", "a"], "metadata": {"licence": "None specified", "description": "<p>First question of exercise 1</p>"}, "type": "question"}]}], "allowPrinting": true, "navigation": {"allowregen": false, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": true, "showresultspage": "oncompletion", "navigatemode": "sequence", "onleave": {"action": "none", "message": ""}, "preventleave": false, "startpassword": ""}, "timing": {"allowPause": false, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "feedback": {"showactualmark": true, "showtotalmark": false, "showanswerstate": true, "allowrevealanswer": true, "advicethreshold": 0, "intro": "<p>You can type your solutions in the gaps. Sometimes it is just a real number but it is also possible to use mathematical expression as for example&nbsp;<em>2x+3i&nbsp;</em>or&nbsp;<br />2$\\pi$ (just type \"pi\"). You may also use the basic functions in mathematical expression like&nbsp;<em>sin, cos, exp&nbsp;</em>(just type \"sin\"). In some cases you have to give&nbsp;<br />an answer or a special keyword; for example in order to identify a geometrical appearance. The software can identify the right prompts like for example \"parabola\".</p>\n<p></p>", "reviewshowscore": true, "reviewshowfeedback": true, "reviewshowexpectedanswer": true, "reviewshowadvice": true, "feedbackmessages": [], "enterreviewmodeimmediately": true, "showexpectedanswerswhen": "inreview", "showpartfeedbackmessageswhen": "always", "showactualmarkwhen": "always", "showtotalmarkwhen": "oncompletion", "showanswerstatewhen": "always", "showadvicewhen": "inreview"}, "type": "exam", "contributors": [{"name": "seb SEE", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1836/"}, {"name": "Philipp Bucher", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2658/"}], "extensions": ["geogebra"], "custom_part_types": [], "resources": [["question-resources/solution1.PNG", "/srv/numbas/media/question-resources/solution1.PNG"], ["question-resources/solution2.PNG", "/srv/numbas/media/question-resources/solution2.PNG"], ["question-resources/solution3.PNG", "/srv/numbas/media/question-resources/solution3.PNG"], ["question-resources/solution4.PNG", "/srv/numbas/media/question-resources/solution4.PNG"], ["question-resources/solution2.1.PNG", "/srv/numbas/media/question-resources/solution2.1.PNG"], ["question-resources/solution2.2.PNG", "/srv/numbas/media/question-resources/solution2.2.PNG"], ["question-resources/solution2.3.PNG", "/srv/numbas/media/question-resources/solution2.3.PNG"], ["question-resources/solution2.4.PNG", "/srv/numbas/media/question-resources/solution2.4.PNG"], ["question-resources/solution3.1.PNG", "/srv/numbas/media/question-resources/solution3.1.PNG"], ["question-resources/solution4.1.PNG", "/srv/numbas/media/question-resources/solution4.1.PNG"], ["question-resources/solution4.2.PNG", "/srv/numbas/media/question-resources/solution4.2.PNG"], ["question-resources/solution4.3.PNG", "/srv/numbas/media/question-resources/solution4.3.PNG"], ["question-resources/solution5.1.PNG", "/srv/numbas/media/question-resources/solution5.1.PNG"], ["question-resources/solution5.2.PNG", "/srv/numbas/media/question-resources/solution5.2.PNG"]]}