// Numbas version: exam_results_page_options
{"name": "Harry's copy of Matthew's copy of Complex number arithmetic", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variablesTest": {"maxRuns": 100, "condition": ""}, "functions": {}, "statement": "<p>Given the complex numbers</p>\n<p>\\[z_1=\\var{z1},\\quad z_2=\\var{z2},&nbsp;\\quad&nbsp;z_3=\\var{z3}, \\quad&nbsp;z_4=\\var{z4},\\]</p>\n<p>calculate the following, writing your answers in Cartesian/rectangular form&nbsp; ($a+bi$), correct to 2 dp, if you have more than two decimal places in your answers).</p>", "variable_groups": [], "preamble": {"css": "", "js": ""}, "variables": {"re_z3onz4": {"definition": "precround(re(z3/z4),3)", "templateType": "anything", "group": "Ungrouped variables", "description": "", "name": "re_z3onz4"}, "z3": {"definition": "random(-10..10)+random(-10..10 except 0)i", "templateType": "anything", "group": "Ungrouped variables", "description": "", "name": "z3"}, "z1minusz2": {"definition": "z1-z2", "templateType": "anything", "group": "Ungrouped variables", "description": "", "name": "z1minusz2"}, "z1z3": {"definition": "z1*z3", "templateType": "anything", "group": "Ungrouped variables", "description": "", "name": "z1z3"}, "modz4sq": {"definition": "z4*z4bar", "templateType": "anything", "group": "Ungrouped variables", "description": "", "name": "modz4sq"}, "z3z4bar": {"definition": "z3*z4bar", "templateType": "anything", "group": "Ungrouped variables", "description": "", "name": "z3z4bar"}, "z2": {"definition": "random(-10..10)+random(-10..10 except 0)i", "templateType": "anything", "group": "Ungrouped variables", "description": "", "name": "z2"}, "z4": {"definition": "random(-10..10)+random(-10..10except 0)i", "templateType": "anything", "group": "Ungrouped variables", "description": "", "name": "z4"}, "z4bar": {"definition": "conj(z4)", "templateType": "anything", "group": "Ungrouped variables", "description": "", "name": "z4bar"}, "z1plusz2": {"definition": "z1+z2", "templateType": "anything", "group": "Ungrouped variables", "description": "", "name": "z1plusz2"}, "im_z3onz4": {"definition": "precround(im(z3/z4),3)", "templateType": "anything", "group": "Ungrouped variables", "description": "", "name": "im_z3onz4"}, "z1": {"definition": "random(-10..10)+random(-10..10 except 0)i", "templateType": "anything", "group": "Ungrouped variables", "description": "", "name": "z1"}}, "tags": [], "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>", "extensions": [], "rulesets": {}, "parts": [{"customMarkingAlgorithm": "", "marks": 1, "answer": "{z1plusz2}", "prompt": "<p>$z_1+z_2=$</p>", "failureRate": 1, "variableReplacementStrategy": "originalfirst", "checkVariableNames": false, "unitTests": [], "vsetRange": [0, 1], "maxlength": {"message": "<p>Incorrect Input</p>", "length": "7", "partialCredit": 0}, "vsetRangePoints": 5, "expectedVariableNames": [], "scripts": {}, "type": "jme", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "checkingType": "absdiff", "showFeedbackIcon": true, "showPreview": true, "showCorrectAnswer": true, "checkingAccuracy": 0.001}, {"customMarkingAlgorithm": "", "marks": 1, "answer": "{z1minusz2}", "prompt": "<p>$z_1-z_2=$</p>", "failureRate": 1, "variableReplacementStrategy": "originalfirst", "checkVariableNames": false, "unitTests": [], "vsetRange": [0, 1], "maxlength": {"message": "<p>Incorrect Input</p>", "length": "7", "partialCredit": 0}, "vsetRangePoints": 5, "expectedVariableNames": [], "scripts": {}, "type": "jme", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "checkingType": "absdiff", "showFeedbackIcon": true, "showPreview": true, "showCorrectAnswer": true, "checkingAccuracy": 0.001}, {"customMarkingAlgorithm": "", "marks": 1, "answer": "{z1z3}", "prompt": "<p>$z_1z_3=$</p>", "notallowed": {"message": "", "showStrings": false, "partialCredit": 0, "strings": ["*"]}, "vsetRange": [0, 1], "maxlength": {"message": "<p>Incorrect Input</p>", "length": "7", "partialCredit": 0}, "scripts": {}, "type": "jme", "showPreview": true, "showCorrectAnswer": true, "checkingType": "absdiff", "variableReplacementStrategy": "originalfirst", "failureRate": 1, "unitTests": [], "vsetRangePoints": 5, "variableReplacements": [], "expectedVariableNames": [], "checkingAccuracy": 0.001, "extendBaseMarkingAlgorithm": true, "checkVariableNames": false, "showFeedbackIcon": true}, {"customMarkingAlgorithm": "", "marks": 1, "answer": "{re_z3onz4}+{im_z3onz4}i", "prompt": "<p>$\\displaystyle\\frac{z_3}{z_4}=$</p>", "notallowed": {"message": "", "showStrings": false, "partialCredit": 0, "strings": ["/"]}, "vsetRange": [0, 1], "maxlength": {"message": "<p>Incorrect Input</p>", "length": "0", "partialCredit": 0}, "scripts": {}, "type": "jme", "showPreview": true, "showCorrectAnswer": true, "checkingType": "absdiff", "variableReplacementStrategy": "originalfirst", "failureRate": 1, "unitTests": [], "vsetRangePoints": 5, "variableReplacements": [], "expectedVariableNames": [], "checkingAccuracy": 0.001, "extendBaseMarkingAlgorithm": true, "checkVariableNames": false, "showFeedbackIcon": true}], "ungrouped_variables": ["z1", "z2", "z3", "z4", "z4bar", "z3z4bar", "modz4sq", "re_z3onz4", "im_z3onz4", "z1plusz2", "z1minusz2", "z1z3"], "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"}, "name": "Harry's copy of Matthew's copy of Complex number arithmetic", "type": "question", "contributors": [{"name": "Harry Flynn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/976/"}]}]}], "contributors": [{"name": "Harry Flynn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/976/"}]}