// Numbas version: exam_results_page_options
{"name": "Maria's copy of Arithmetics of complex numbers IV", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus", "!collectlikefractions"]}, "extensions": [], "variables": {"c2": {"name": "c2", "description": "", "definition": "random(1..5)", "group": "Ungrouped variables", "templateType": "anything"}, "z3": {"name": "z3", "description": "", "definition": "rz3+s1*random(1..9)*i", "group": "Ungrouped variables", "templateType": "anything"}, "rz3": {"name": "rz3", "description": "", "definition": "if(a3=re(z1),a3+random(1,-1),a3)", "group": "Ungrouped variables", "templateType": "anything"}, "c1": {"name": "c1", "description": "", "definition": "s3*random(1..9)", "group": "Ungrouped variables", "templateType": "anything"}, "s4": {"name": "s4", "description": "", "definition": "random(1,-1)", "group": "Ungrouped variables", "templateType": "anything"}, "s2": {"name": "s2", "description": "", "definition": "random(1,-1)", "group": "Ungrouped variables", "templateType": "anything"}, "a3": {"name": "a3", "description": "", "definition": "s3*random(1..9)", "group": "Ungrouped variables", "templateType": "anything"}, "z1": {"name": "z1", "description": "", "definition": "s2*random(1..9)+s1*random(1..9)*i", "group": "Ungrouped variables", "templateType": "anything"}, "z2": {"name": "z2", "description": "", "definition": "re(z1)+s2*random(1,2)+s4*random(1..9)*i", "group": "Ungrouped variables", "templateType": "anything"}, "s3": {"name": "s3", "description": "", "definition": "random(1,-1)", "group": "Ungrouped variables", "templateType": "anything"}, "s1": {"name": "s1", "description": "", "definition": "random(1,-1)", "group": "Ungrouped variables", "templateType": "anything"}}, "variablesTest": {"maxRuns": 100, "condition": ""}, "tags": ["algebra of complex numbers", "checked2015", "complex arithmetic", "complex numbers", "division of complex numbers", "inverse of complex numbers", "multiplication of complex numbers", "product of complex numbers"], "ungrouped_variables": ["s3", "s2", "s1", "s4", "a3", "rz3", "c2", "c1", "z1", "z2", "z3"], "preamble": {"js": "", "css": ""}, "variable_groups": [], "metadata": {"description": "<p>Composite multiplication and division of complex numbers. Two parts.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "advice": "\n  <p>a) <br/>\\[\\begin{eqnarray*}z=\\simplify[!collectNumbers]{({z3}*{z2})/{z1}} &amp;=&amp;\\simplify[!collectNumbers]{({z3}*{z2}*{conj(z1)})/({z1}*{conj(z1)})}\\\\ &amp;=&amp;\\simplify[!collectNumbers]{({z3*z2}*{conj(z1)})/({abs(z1)^2})}\\\\ &amp;=&amp;\\simplify[!collectNumbers]{{z3*z2*conj(z1)}/{abs(z1)^2}}\\\\ &amp;=&amp; \\simplify[std]{{re(z3*z2*conj(z1))}/{abs(z1)^2}+{im(z3*z2*conj(z1))}/{abs(z1)^2}*i} \\end{eqnarray*} \\]</p>\n  <p>b)<br/>\\[\\begin{eqnarray*}z= \\simplify[!collectNumbers]{({z2}*{z1})}(\\var{z3})^{-1}&nbsp;&amp;=&amp; \\simplify[!collectNumbers]{({z2}*{z1})/{z3}}\\\\ &amp;=&amp;\\simplify[!collectNumbers]{({z2}*{z1}*{conj(z3)})/({z3}*{conj(z3)})}\\\\ &amp;=&amp;\\simplify[!collectNumbers]{({z2*z1}*{conj(z3)})/({abs(z3)^2})}\\\\ &amp;=&amp;\\simplify[!collectNumbers]{{z2*z1*conj(z3)}/{abs(z3)^2}}\\\\ &amp;=&amp; \\simplify[std]{{re(z2*z1*conj(z3))}/{abs(z3)^2}+{im(z2*z1*conj(z3))}/{abs(z3)^2}*i} \\end{eqnarray*} \\]</p>\n  ", "name": "Maria's copy of Arithmetics of complex numbers IV", "statement": "<p>Express the following complex numbers $z$ in the form $a+bi$.</p>\n<p>Input $a$ and $b$ as fractions and not as decimals.</p>", "parts": [{"showCorrectAnswer": true, "unitTests": [], "gaps": [{"vsetRange": [0, 1], "showCorrectAnswer": true, "unitTests": [], "variableReplacementStrategy": "originalfirst", "marks": 1, "showPreview": true, "type": "jme", "mustmatchpattern": {"partialCredit": 0, "message": "Your answer is not in the form $a+bi$.", "nameToCompare": "", "pattern": "`+-((integer:$n/integer:$n`?))`? + ((`+-integer:$n`?/integer:$n`?)*i `| `+-i)`?"}, "failureRate": 1, "variableReplacements": [], "customName": "", "answer": "{re(conj(z1)*z3*z2)}/{abs(z1)^2}+{im(conj(z1)*z3*z2)}/{abs(z1)^2}*i", "checkingAccuracy": 0.001, "answerSimplification": "std", "showFeedbackIcon": true, "valuegenerators": [], "checkVariableNames": false, "useCustomName": false, "checkingType": "absdiff", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "scripts": {}, "vsetRangePoints": 5}], "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "\n      <p>\\[\\displaystyle z=\\simplify[!collectNumbers]{({z3}*{z2})/{z1}}\\]</p>\n      <p>$z=\\;\\;$[[0]].</p>\n      ", "marks": 0, "useCustomName": false, "type": "gapfill", "sortAnswers": false, "extendBaseMarkingAlgorithm": true, "scripts": {}, "customMarkingAlgorithm": "", "variableReplacements": [], "customName": ""}, {"showCorrectAnswer": true, "unitTests": [], "gaps": [{"vsetRange": [0, 1], "showCorrectAnswer": true, "unitTests": [], "variableReplacementStrategy": "originalfirst", "marks": 1, "showPreview": true, "type": "jme", "mustmatchpattern": {"partialCredit": 0, "message": "Your answer is not in the form $a+bi$.", "nameToCompare": "", "pattern": "`+-((integer:$n/integer:$n`?))`? + ((`+-integer:$n`?/integer:$n`?)*i `| `+-i)`?"}, "failureRate": 1, "variableReplacements": [], "customName": "", "answer": "{re(conj(z3)*z1*z2)}/{abs(z3)^2}+{im(conj(z3)*z1*z2)}/{abs(z3)^2}*i", "checkingAccuracy": 0.001, "answerSimplification": "std", "showFeedbackIcon": true, "valuegenerators": [], "checkVariableNames": false, "useCustomName": false, "checkingType": "absdiff", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "scripts": {}, "vsetRangePoints": 5}], "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "\n      <p>\\[\\displaystyle z=\\simplify[!collectNumbers]{({z2}*{z1})}(\\var{z3})^{-1}\\]</p>\n      <p>$z=\\;\\;$[[0]].</p>\n      ", "marks": 0, "useCustomName": false, "type": "gapfill", "sortAnswers": false, "extendBaseMarkingAlgorithm": true, "scripts": {}, "customMarkingAlgorithm": "", "variableReplacements": [], "customName": ""}], "functions": {}, "type": "question", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Maria Aneiros", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3388/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Maria Aneiros", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3388/"}]}