// Numbas version: exam_results_page_options
{"name": "Complex number multiplication & division", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variablesTest": {"maxRuns": 100, "condition": ""}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Complex number multiplication &amp; division</p>"}, "advice": "<p>\\(\\frac{Z_1*Z_2}{Z_3}=\\frac{(\\var{x1}+\\var{y1}j)(\\var{x2}+\\var{y2}j)}{\\var{x3}+\\var{y3}j}\\)</p>\n<p style=\"padding-left: 60px;\">=\\(\\frac{\\simplify{{x1}*{x2}}+\\simplify{{x1}*{y2}}j+\\simplify{{y1}*{x2}}j+\\simplify{{y1}*{y2}}j^{2}}{\\var{x3}+\\var{y3}j}\\)</p>\n<p style=\"padding-left: 60px;\">=\\(\\frac{\\simplify{{x1}*{x2}}+\\simplify{{x1}*{y2}+{y1}*{x2}}j-\\simplify{{y1}*{y2}}}{\\var{x3}+\\var{y3}j}\\)</p>\n<p style=\"padding-left: 60px;\">=\\(\\frac{\\simplify{{x1}*{x2}-{y1}*{y2}}+\\simplify{{x1}*{y2}+{y1}*{x2}}j}{\\var{x3}+\\var{y3}j}\\)</p>\n<p style=\"padding-left: 60px;\">=\\(\\frac{\\simplify{{x1}*{x2}-{y1}*{y2}}+\\simplify{{x1}*{y2}+{y1}*{x2}}j}{\\var{x3}+\\var{y3}j}\\frac{\\var{x3}-\\var{y3}j}{\\var{x3}-\\var{y3}j}\\)</p>\n<p style=\"padding-left: 60px;\">=\\(\\frac{\\simplify{({x1}*{x2}-{y1}*{y2})*{x3}}-(\\simplify{({x1}*{x2}-{y1}*{y2})*{y3}}j)+(\\simplify{({x1}*{y2}+{y1}*{x2})*{x3}}j)-\\simplify{({x1}*{y2}+{y1}*{x2})*{y3}}j^{2}}{\\var{x3}^{2}+\\var{y3}^{2}}\\)</p>\n<p style=\"padding-left: 60px;\">=\\(\\frac{\\simplify{({x1}*{x2}-{y1}*{y2})*{x3}+({x1}*{y2}+{y1}*{x2})*{y3}}+\\simplify{({x1}*{y2}+{y1}*{x2})*{x3}-({x1}*{x2}-{y1}*{y2})*{y3}}j}{\\simplify{{x3}^{2}+{y3}^{2}}}\\)</p>\n<p style=\"padding-left: 60px;\">=\\(\\var{A}+\\var{B}j\\)&nbsp;</p>", "ungrouped_variables": ["x1", "x2", "x3", "y1", "y2", "y3", "A", "B"], "tags": [], "statement": "<p>Given three complex numbers \\(Z_{1}=\\var{x1}+\\var{y1}j\\), &nbsp; &nbsp;\\(Z_{2}=\\var{x2}+\\var{y2}j\\) &nbsp; &nbsp;and &nbsp;&nbsp;\\(Z_{3}=\\var{x3}+\\var{y3}j\\)</p>", "functions": {}, "variable_groups": [], "extensions": [], "parts": [{"scripts": {}, "prompt": "<p>&nbsp;If &nbsp; \\(\\frac{Z_{1}*Z_2}{Z_3}=A+Bj\\)</p>\n<p>Input the value for \\(A\\) &nbsp;&nbsp;[[0]]</p>\n<p>Input the value for \\(B\\) &nbsp;&nbsp;[[1]]</p>", "variableReplacementStrategy": "originalfirst", "marks": 0, "type": "gapfill", "showFeedbackIcon": true, "variableReplacements": [], "gaps": [{"correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "minValue": "{A}", "showPrecisionHint": true, "precisionType": "dp", "showCorrectAnswer": true, "scripts": {}, "precision": "2", "precisionPartialCredit": 0, "correctAnswerStyle": "plain", "marks": 1, "type": "numberentry", "strictPrecision": false, "maxValue": "{A}", "variableReplacements": [], "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "showFeedbackIcon": true}, {"correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "minValue": "{B}", "showPrecisionHint": true, "precisionType": "dp", "showCorrectAnswer": true, "scripts": {}, "precision": "2", "precisionPartialCredit": 0, "correctAnswerStyle": "plain", "marks": 1, "type": "numberentry", "strictPrecision": false, "maxValue": "{B}", "variableReplacements": [], "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "showFeedbackIcon": true}], "showCorrectAnswer": true}], "rulesets": {}, "variables": {"A": {"group": "Ungrouped variables", "name": "A", "description": "", "templateType": "anything", "definition": "(({x1}*{x2}-{y1}*{y2})*{x3}+({x2}*{y1}+{x1}*{y2})*{y3})/({x3}^2+{y3}^2)"}, "B": {"group": "Ungrouped variables", "name": "B", "description": "", "templateType": "anything", "definition": "(-({x1}*{x2}-{y1}*{y2})*{y3}+({x2}*{y1}+{x1}*{y2})*{x3})/({x3}^2+{y3}^2)"}, "x3": {"group": "Ungrouped variables", "name": "x3", "description": "", "templateType": "randrange", "definition": "random(3..8#1)"}, "y1": {"group": "Ungrouped variables", "name": "y1", "description": "", "templateType": "randrange", "definition": "random(2..10#1)"}, "x1": {"group": "Ungrouped variables", "name": "x1", "description": "", "templateType": "randrange", "definition": "random(2..10#1)"}, "y3": {"group": "Ungrouped variables", "name": "y3", "description": "", "templateType": "randrange", "definition": "random(2..15#1)"}, "x2": {"group": "Ungrouped variables", "name": "x2", "description": "", "templateType": "randrange", "definition": "random(1..9#1)"}, "y2": {"group": "Ungrouped variables", "name": "y2", "description": "", "templateType": "randrange", "definition": "random(1..12#1)"}}, "name": "Complex number multiplication & division", "preamble": {"js": "", "css": ""}, "type": "question", "contributors": [{"name": "Michael Proudman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/269/"}]}]}], "contributors": [{"name": "Michael Proudman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/269/"}]}