// Numbas version: exam_results_page_options {"name": "Complex number arithmetic", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Complex number arithmetic", "parts": [{"vsetrangepoints": 5, "checkvariablenames": false, "checkingtype": "absdiff", "marks": 1, "prompt": "
$z_1+z_2=$
", "scripts": {}, "answer": "{z1plusz2}", "showFeedbackIcon": true, "showpreview": true, "showCorrectAnswer": true, "vsetrange": [0, 1], "variableReplacementStrategy": "originalfirst", "type": "jme", "expectedvariablenames": [], "checkingaccuracy": 0.001, "variableReplacements": []}, {"vsetrangepoints": 5, "checkvariablenames": false, "checkingtype": "absdiff", "marks": "1", "prompt": "$z_1-z_2=$
", "scripts": {}, "answer": "{z1minusz2}", "showFeedbackIcon": true, "showpreview": true, "showCorrectAnswer": true, "vsetrange": [0, 1], "variableReplacementStrategy": "originalfirst", "type": "jme", "expectedvariablenames": [], "checkingaccuracy": 0.001, "variableReplacements": []}, {"vsetrangepoints": 5, "checkvariablenames": false, "checkingtype": "absdiff", "marks": 1, "prompt": "$z_1z_3=$
", "scripts": {}, "answer": "{z1z3}", "showFeedbackIcon": true, "showpreview": true, "showCorrectAnswer": true, "vsetrange": [0, 1], "variableReplacementStrategy": "originalfirst", "type": "jme", "expectedvariablenames": [], "checkingaccuracy": 0.001, "variableReplacements": []}], "functions": {}, "preamble": {"css": "", "js": ""}, "variablesTest": {"condition": "", "maxRuns": 100}, "rulesets": {}, "variable_groups": [], "extensions": [], "advice": "\\[z_1+z_2=(\\var{z1})+(\\var{z2})=\\simplify{{z1}+{z2}}\\]
\n\\[z_1-z_2=(\\var{z1})-(\\var{z2})=\\simplify{{z1}-{z2}}\\]
\n\\[z_1z_3=(\\var{z1})(\\var{z3})=\\var{z1z3}\\]
\n", "statement": "This question will help you to practice adding, subtracting, multiplying and dividing complex numbers in Cartesian/rectangular form. If you wish, you might like to watch this video which explains these operations and how to do problems like these.
\n\nGiven the complex numbers
\n\\[z_1=\\var{z1},\\quad z_2=\\var{z2}, \\quad z_3=\\var{z3}, \\quad z_4=\\var{z4},\\]
\ncalculate the following (write your answers in Cartesian/rectangular form). Where necessary, round off your answers to 2 decimal places.
", "variables": {"z4": {"definition": "random(-10..10)+random(-10..10)i", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "z4"}, "modz4sq": {"definition": "z4*z4bar", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "modz4sq"}, "z3": {"definition": "random(-10..10)+random(-10..10)i", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "z3"}, "z1": {"definition": "random(-10..10)+random(-10..10)i", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "z1"}, "re_z3onz4": {"definition": "re(z3/z4)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "re_z3onz4"}, "z2": {"definition": "random(-10..10)+random(-10..10)i", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "z2"}, "z3z4bar": {"definition": "z3*z4bar", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "z3z4bar"}, "z1minusz2": {"definition": "z1-z2", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "z1minusz2"}, "im_z3onz4": {"definition": "im(z3/z4)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "im_z3onz4"}, "z1z3": {"definition": "z1*z3", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "z1z3"}, "z4bar": {"definition": "conj(z4)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "z4bar"}, "z1plusz2": {"definition": "z1+z2", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "z1plusz2"}}, "tags": [], "metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": "This question provides practice at adding, subtracting, dividing and multiplying complex numbers in rectangular form.
"}, "ungrouped_variables": ["z1", "z2", "z3", "z4", "z4bar", "z3z4bar", "modz4sq", "re_z3onz4", "im_z3onz4", "z1plusz2", "z1minusz2", "z1z3"], "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/"}]}