// Numbas version: exam_results_page_options {"name": "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": [{"metadata": {"description": "
This question provides practice at adding, subtracting, dividing and multiplying complex numbers in rectangular form.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "name": "Matthew's copy of Complex number arithmetic", "variable_groups": [], "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\n\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).
", "functions": {}, "preamble": {"css": "", "js": ""}, "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\\[\\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}\\]
", "tags": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"z2": {"group": "Ungrouped variables", "definition": "random(-10..10)+random(-10..10)i", "name": "z2", "templateType": "anything", "description": ""}, "z1": {"group": "Ungrouped variables", "definition": "random(-10..10)+random(-10..10)i", "name": "z1", "templateType": "anything", "description": ""}, "im_z3onz4": {"group": "Ungrouped variables", "definition": "im(z3/z4)", "name": "im_z3onz4", "templateType": "anything", "description": ""}, "z1plusz2": {"group": "Ungrouped variables", "definition": "z1+z2", "name": "z1plusz2", "templateType": "anything", "description": ""}, "z4": {"group": "Ungrouped variables", "definition": "random(-10..10)+random(-10..10)i", "name": "z4", "templateType": "anything", "description": ""}, "z1minusz2": {"group": "Ungrouped variables", "definition": "z1-z2", "name": "z1minusz2", "templateType": "anything", "description": ""}, "z1z3": {"group": "Ungrouped variables", "definition": "z1*z3", "name": "z1z3", "templateType": "anything", "description": ""}, "re_z3onz4": {"group": "Ungrouped variables", "definition": "re(z3/z4)", "name": "re_z3onz4", "templateType": "anything", "description": ""}, "z3z4bar": {"group": "Ungrouped variables", "definition": "z3*z4bar", "name": "z3z4bar", "templateType": "anything", "description": ""}, "modz4sq": {"group": "Ungrouped variables", "definition": "z4*z4bar", "name": "modz4sq", "templateType": "anything", "description": ""}, "z3": {"group": "Ungrouped variables", "definition": "random(-10..10)+random(-10..10)i", "name": "z3", "templateType": "anything", "description": ""}, "z4bar": {"group": "Ungrouped variables", "definition": "conj(z4)", "name": "z4bar", "templateType": "anything", "description": ""}}, "extensions": [], "rulesets": {}, "parts": [{"showFeedbackIcon": true, "checkvariablenames": false, "vsetrange": [0, 1], "answer": "{z1plusz2}", "expectedvariablenames": [], "marks": 1, "vsetrangepoints": 5, "checkingaccuracy": 0.001, "showCorrectAnswer": true, "scripts": {}, "prompt": "$z_1+z_2=$
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", "type": "jme", "variableReplacementStrategy": "originalfirst", "checkingtype": "absdiff", "showpreview": true, "variableReplacements": []}, {"showFeedbackIcon": true, "checkvariablenames": false, "vsetrange": [0, 1], "answer": "{re_z3onz4}+{im_z3onz4}i", "expectedvariablenames": [], "marks": 1, "vsetrangepoints": 5, "checkingaccuracy": 0.001, "showCorrectAnswer": true, "scripts": {}, "prompt": "$\\displaystyle\\frac{z_3}{z_4}=$
", "type": "jme", "variableReplacementStrategy": "originalfirst", "checkingtype": "absdiff", "showpreview": true, "variableReplacements": []}], "ungrouped_variables": ["z1", "z2", "z3", "z4", "z4bar", "z3z4bar", "modz4sq", "re_z3onz4", "im_z3onz4", "z1plusz2", "z1minusz2", "z1z3"], "type": "question", "contributors": [{"name": "Matthew Blacklock", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2386/"}]}]}], "contributors": [{"name": "Matthew Blacklock", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2386/"}]}