// Numbas version: exam_results_page_options
{"name": "Complex Numbers 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["z1", "z2", "z3", "z4", "z4bar", "z3z4bar", "modz4sq", "re_z3onz4", "im_z3onz4", "z1plusz2", "z1minusz2", "z1z3"], "name": "Complex Numbers 2", "tags": [], "preamble": {"css": "", "js": ""}, "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>", "rulesets": {}, "parts": [{"vsetrangepoints": 5, "prompt": "<p>$z_1+z_2=$</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "{z1plusz2}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "prompt": "<p>$z_1-z_2=$</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "{z1minusz2}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "prompt": "<p>$z_1z_3=$</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "{z1z3}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "prompt": "<p>$\\displaystyle\\frac{z_3}{z_4}=$</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "{re_z3onz4}+{im_z3onz4}i", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "extensions": [], "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 (write your answers in Cartesian/rectangular form).</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"im_z3onz4": {"definition": "im(z3/z4)", "templateType": "anything", "group": "Ungrouped variables", "name": "im_z3onz4", "description": ""}, "z1z3": {"definition": "z1*z3", "templateType": "anything", "group": "Ungrouped variables", "name": "z1z3", "description": ""}, "z3z4bar": {"definition": "z3*z4bar", "templateType": "anything", "group": "Ungrouped variables", "name": "z3z4bar", "description": ""}, "modz4sq": {"definition": "z4*z4bar", "templateType": "anything", "group": "Ungrouped variables", "name": "modz4sq", "description": ""}, "z3": {"definition": "random(-10..10)+random(-10..10)i", "templateType": "anything", "group": "Ungrouped variables", "name": "z3", "description": ""}, "z4": {"definition": "random(-10..10)+random(-10..10)i", "templateType": "anything", "group": "Ungrouped variables", "name": "z4", "description": ""}, "z4bar": {"definition": "conj(z4)", "templateType": "anything", "group": "Ungrouped variables", "name": "z4bar", "description": ""}, "re_z3onz4": {"definition": "re(z3/z4)", "templateType": "anything", "group": "Ungrouped variables", "name": "re_z3onz4", "description": ""}, "z1minusz2": {"definition": "z1-z2", "templateType": "anything", "group": "Ungrouped variables", "name": "z1minusz2", "description": ""}, "z1": {"definition": "random(-10..10)+random(-10..10)i", "templateType": "anything", "group": "Ungrouped variables", "name": "z1", "description": ""}, "z2": {"definition": "random(-10..10)+random(-10..10)i", "templateType": "anything", "group": "Ungrouped variables", "name": "z2", "description": ""}, "z1plusz2": {"definition": "z1+z2", "templateType": "anything", "group": "Ungrouped variables", "name": "z1plusz2", "description": ""}}, "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Mark Hodds", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/510/"}]}]}], "contributors": [{"name": "Mark Hodds", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/510/"}]}