// Numbas version: exam_results_page_options
{"name": "Maria's copy of Complex number arithmetic: multiply and divide", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"extensions": [], "variables": {"b": {"name": "b", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(-10..10)+random(-10..10)i"}, "a": {"name": "a", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(-10..10)+random(-10..10)i"}, "c": {"name": "c", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(-10..10)+random(-10..10)i"}, "d": {"name": "d", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(-10..10)+random(-10..10)i"}, "twocans": {"name": "twocans", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "(a*conj(b))"}}, "variablesTest": {"maxRuns": 100, "condition": ""}, "tags": [], "rulesets": {}, "parts": [{"stepsPenalty": 0, "showCorrectAnswer": true, "vsetrangepoints": 5, "vsetrange": [0, 1], "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "showFeedbackIcon": true, "notallowed": {"strings": ["(", ")"], "partialCredit": 0, "message": "<p>No brackets are required or allowed.</p>", "showStrings": false}, "steps": [{"prompt": "<p>Expand the brackets $(\\var{a})(\\var{b})$.</p>", "marks": 0, "type": "information", "scripts": {}, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true}, {"prompt": "<p>Simplify using the fact $i^2=-1$.</p>", "marks": 0, "type": "information", "scripts": {}, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true}], "checkingaccuracy": 0.001, "prompt": "<p>$ab=$</p>", "marks": "2", "checkingtype": "absdiff", "type": "jme", "scripts": {}, "variableReplacements": [], "showpreview": false, "answer": "{a*b}", "checkvariablenames": false}, {"showCorrectAnswer": true, "vsetrangepoints": 5, "vsetrange": [0, 1], "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "showFeedbackIcon": true, "notallowed": {"strings": ["(", ")"], "partialCredit": 0, "message": "<p>No brackets are required or allowed.</p>", "showStrings": false}, "checkingaccuracy": 0.001, "prompt": "<p>$ac=$</p>", "marks": "2", "checkingtype": "absdiff", "type": "jme", "scripts": {}, "variableReplacements": [], "showpreview": false, "answer": "{a*c}", "checkvariablenames": false}, {"stepsPenalty": 0, "showCorrectAnswer": true, "vsetrangepoints": 5, "vsetrange": [0, 1], "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "showFeedbackIcon": true, "notallowed": {"strings": ["(", ")"], "partialCredit": 0, "message": "<p>No brackets are required or allowed.</p>", "showStrings": false}, "steps": [{"showCorrectAnswer": true, "vsetrangepoints": 5, "vsetrange": [0, 1], "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "showFeedbackIcon": true, "checkingaccuracy": 0.001, "prompt": "<p>What is the complex conjugate of $b$?</p>\n<p>$\\overline{b}=$</p>", "marks": 1, "checkingtype": "absdiff", "type": "jme", "scripts": {}, "variableReplacements": [], "showpreview": false, "answer": "{conj(b)}", "checkvariablenames": false}, {"showCorrectAnswer": true, "vsetrangepoints": 5, "vsetrange": [0, 1], "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "showFeedbackIcon": true, "checkingaccuracy": 0.001, "prompt": "<p>Multiply the numerator ($\\var{a}$) by $\\overline{b}$.</p>", "marks": 1, "checkingtype": "absdiff", "type": "jme", "scripts": {}, "variableReplacements": [], "showpreview": false, "answer": "{a*conj(b)}", "checkvariablenames": false}, {"showCorrectAnswer": true, "vsetrangepoints": 5, "vsetrange": [0, 1], "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "showFeedbackIcon": true, "checkingaccuracy": 0.001, "prompt": "<p>Multiply the denominator ($\\var{b}$) by $\\overline{b}$.</p>", "marks": 1, "checkingtype": "absdiff", "type": "jme", "scripts": {}, "variableReplacements": [], "showpreview": false, "answer": "{b*conj(b)}", "checkvariablenames": false}, {"prompt": "<p>Now divide your two answers.</p>\n<p>\\[\\frac{a}{b}=\\frac{a\\overline{b}}{b\\overline{b}}\\]</p>", "marks": 0, "type": "information", "scripts": {}, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true}], "checkingaccuracy": 0.001, "prompt": "<p>$\\frac{a}{b}=$</p>", "marks": "2", "checkingtype": "absdiff", "type": "jme", "scripts": {}, "variableReplacements": [], "showpreview": false, "answer": "{a/b}", "checkvariablenames": false}, {"showCorrectAnswer": true, "vsetrangepoints": 5, "vsetrange": [0, 1], "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "showFeedbackIcon": true, "notallowed": {"strings": ["(", ")"], "partialCredit": 0, "message": "<p>No brackets are required or allowed.</p>", "showStrings": false}, "checkingaccuracy": 0.001, "prompt": "<p>$\\frac{a}{c}=$</p>", "marks": "2", "checkingtype": "absdiff", "type": "jme", "scripts": {}, "variableReplacements": [], "showpreview": false, "answer": "{a/c}", "checkvariablenames": false}, {"showCorrectAnswer": true, "vsetrangepoints": 5, "vsetrange": [0, 1], "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "showFeedbackIcon": true, "notallowed": {"strings": ["(", ")"], "partialCredit": 0, "message": "<p>No brackets are required or allowed.</p>", "showStrings": false}, "checkingaccuracy": 0.001, "prompt": "<p>$ad=$</p>", "marks": "2", "checkingtype": "absdiff", "type": "jme", "scripts": {}, "variableReplacements": [], "showpreview": false, "answer": "{a*d}", "checkvariablenames": false}, {"showCorrectAnswer": true, "vsetrangepoints": 5, "vsetrange": [0, 1], "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "showFeedbackIcon": true, "notallowed": {"strings": ["(", ")"], "partialCredit": 0, "message": "<p>No brackets are required or allowed.</p>", "showStrings": false}, "checkingaccuracy": 0.001, "prompt": "<p>$\\frac{b}{d}=$</p>", "marks": "2", "checkingtype": "absdiff", "type": "jme", "scripts": {}, "variableReplacements": [], "showpreview": false, "answer": "{b/d}", "checkvariablenames": false}], "ungrouped_variables": ["a", "b", "c", "d", "twocans"], "variable_groups": [], "metadata": {"description": "<p>This question provides practice at adding, subtracting, dividing and multiplying complex numbers in rectangular form.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "advice": "<p>\\[z_1+z_2=(\\var{z1})+(\\var{z2})=\\simplify{{z1}+{z2}}\\]</p>\n<p>\\[z_1-z_2=(\\var{z1})-(\\var{z2})=\\simplify{{z1}-{z2}}\\]</p>\n<p>\\[z_1z_3=(\\var{z1})(\\var{z3})=\\var{z1z3}\\]</p>\n<p>\\[\\frac{z_3}{z_4}=\\frac{\\var{z3}}{\\var{z4}}=\\frac{(\\var{z3})(\\var{z4bar})}{(\\var{z4})(\\var{z4bar})}=\\simplify{{z3z4bar}/{modz4sq}}\\approx \\var{re_z3onz4}+\\var{im_z3onz4}\\]</p>", "name": "Maria's copy of Complex number arithmetic: multiply and divide", "statement": "<p>Given the complex numbers</p>\n<p>\\[a=\\var{a},\\quad b=\\var{b},\\quad c=\\var{c},\\quad d=\\var{d},\\]</p>\n<p>calculate the following. Enter your answers in the form</p>\n<p>\\[x+iy\\]</p>", "preamble": {"js": "", "css": ""}, "functions": {}, "type": "question", "contributors": [{"name": "Martin Jones", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/145/"}, {"name": "Maria Aneiros", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3388/"}]}]}], "contributors": [{"name": "Martin Jones", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/145/"}, {"name": "Maria Aneiros", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3388/"}]}