// Numbas version: finer_feedback_settings
{"name": "Luis's copy of Arithmetics of complex numbers II", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variablesTest": {"condition": "", "maxRuns": 100}, "parts": [{"sortAnswers": false, "showFeedbackIcon": true, "scripts": {}, "unitTests": [], "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "gaps": [{"answer": "{a*e6*i}", "checkingType": "absdiff", "answerSimplification": "std", "expectedVariableNames": [], "vsetRangePoints": 5, "checkVariableNames": false, "showFeedbackIcon": true, "notallowed": {"showStrings": false, "partialCredit": 0, "strings": [".", ")", "("], "message": "<p>Input all numbers as fractions or integers. Also do not include brackets in your answers.</p>"}, "scripts": {}, "checkingAccuracy": 0.001, "unitTests": [], "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "showPreview": true, "vsetRange": [0, 1], "variableReplacements": [], "showCorrectAnswer": true, "marks": 1, "failureRate": 1, "type": "jme", "extendBaseMarkingAlgorithm": true}], "variableReplacements": [], "showCorrectAnswer": true, "marks": 0, "type": "gapfill", "prompt": "<p>$\\var{e6*i}(\\simplify[std]{{a}})\\;=\\;$[[0]].</p>", "extendBaseMarkingAlgorithm": true}, {"sortAnswers": false, "showFeedbackIcon": true, "scripts": {}, "unitTests": [], "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "gaps": [{"answer": "({a*z4})", "checkingType": "absdiff", "answerSimplification": "std", "expectedVariableNames": [], "vsetRangePoints": 5, "checkVariableNames": false, "showFeedbackIcon": true, "notallowed": {"showStrings": false, "partialCredit": 0, "strings": [".", ")", "("], "message": "<p>Input all numbers as fractions or integers. Also do not include brackets in your answers.</p>"}, "scripts": {}, "checkingAccuracy": 0.001, "unitTests": [], "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "showPreview": true, "vsetRange": [0, 1], "variableReplacements": [], "showCorrectAnswer": true, "marks": 1, "failureRate": 1, "type": "jme", "extendBaseMarkingAlgorithm": true}], "variableReplacements": [], "showCorrectAnswer": true, "marks": 0, "type": "gapfill", "prompt": "<p>$(\\simplify[std]{{a}})(\\simplify[std]{{z4}})\\;=\\;$[[0]].</p>", "extendBaseMarkingAlgorithm": true}, {"sortAnswers": false, "showFeedbackIcon": true, "scripts": {}, "unitTests": [], "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "gaps": [{"answer": "{(a3 + b3 * i + c3 * i ^ 2 + d3 * i ^ 3)*a}", "checkingType": "absdiff", "expectedVariableNames": [], "vsetRangePoints": 5, "checkVariableNames": false, "showFeedbackIcon": true, "notallowed": {"showStrings": false, "partialCredit": 0, "strings": [".", ")", "("], "message": "<p>Input all numbers as fractions or integers. Also do not include brackets in your answers.</p>"}, "scripts": {}, "checkingAccuracy": 0.001, "unitTests": [], "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "showPreview": true, "vsetRange": [0, 1], "variableReplacements": [], "showCorrectAnswer": true, "marks": 1, "failureRate": 1, "type": "jme", "extendBaseMarkingAlgorithm": true}], "variableReplacements": [], "showCorrectAnswer": true, "marks": 0, "type": "gapfill", "prompt": "<p>$\\simplify[std,!otherNumbers]{{a}*({a3} + {b3} * i + {c3} * i ^ 2 + {d3} * i ^ 3)}\\;=\\;$[[0]].</p>", "extendBaseMarkingAlgorithm": true}, {"sortAnswers": false, "showFeedbackIcon": true, "scripts": {}, "unitTests": [], "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "gaps": [{"answer": "{a*(z1)*(z3)}", "checkingType": "absdiff", "expectedVariableNames": [], "vsetRangePoints": 5, "checkVariableNames": false, "showFeedbackIcon": true, "notallowed": {"showStrings": false, "partialCredit": 0, "strings": [".", ")", "("], "message": "<p>Input all numbers as fractions or integers. Also do not include brackets in your answers.</p>"}, "scripts": {}, "checkingAccuracy": 0.001, "unitTests": [], "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "showPreview": true, "vsetRange": [0, 1], "variableReplacements": [], "showCorrectAnswer": true, "marks": 1, "failureRate": 1, "type": "jme", "extendBaseMarkingAlgorithm": true}], "variableReplacements": [], "showCorrectAnswer": true, "marks": 0, "type": "gapfill", "prompt": "<p>$(\\simplify[std]{{a}})(\\simplify[std]{ {z1}})(\\simplify[std]{ {z3}})\\;=\\;$[[0]].</p>", "extendBaseMarkingAlgorithm": true}], "name": "Luis's copy of Arithmetics of complex numbers II", "ungrouped_variables": ["a", "f6", "s3", "s2", "s1", "d3", "s6", "s5", "s4", "c3", "a3", "b3", "d6", "e6", "z4", "z1", "z2", "z3"], "statement": "<p><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">Encuentre los siguientes n&uacute;meros complejos en la forma $ a + bi \\; $ donde $ a $ y $ b $ son reales.</span></span></p>\n<p><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">Ingresa todos los n&uacute;meros como fracciones o enteros. </span><span style=\"vertical-align: inherit;\">Tampoco incluya corchetes en sus respuestas.</span></span></p>", "preamble": {"css": "", "js": ""}, "variables": {"f6": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "f6", "definition": "s6*random(1..9)"}, "s6": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "s6", "definition": "random(1,-1)"}, "s2": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "s2", "definition": "random(1,-1)"}, "s4": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "s4", "definition": "random(1,-1)"}, "c3": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "c3", "definition": "s3*random(1..9)"}, "e6": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "e6", "definition": "s5*random(3..9)"}, "z2": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "z2", "definition": "s2*random(1..9)+d6*i"}, "z1": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "z1", "definition": "s3*random(1..9)+f6*i"}, "d6": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "d6", "definition": "s4*random(1..9)"}, "s3": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "s3", "definition": "random(1,-1)"}, "s5": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "s5", "definition": "random(1,-1)"}, "a": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "a", "definition": "s1*random(1..9)+s2*random(1..9)*i"}, "s1": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "s1", "definition": "random(1,-1)"}, "a3": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "a3", "definition": "s1*random(1..9)"}, "b3": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "b3", "definition": "s2*random(1..9)"}, "d3": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "d3", "definition": "s4*random(1..9)"}, "z3": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "z3", "definition": "s6*random(1..9)+e6*i"}, "z4": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "z4", "definition": "s6*s2*random(1..9)+s3*s5*random(1..9)*i"}}, "metadata": {"description": "<p>Multiplication and addition of complex numbers. Four parts.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "functions": {}, "variable_groups": [], "advice": "<p>a)</p>\n  <p>The solution is given by:</p>\n  <p><br/>$\\simplify[std]{{e6*i}}(\\simplify[std]{{a}})=\\simplify[std]{{a*e6*i}}$</p>\n  <p><br/>b)</p>\n  <p>$\\simplify[std]{{a}*{z4}={a*z4}}$</p>\n  <p><br/>c) <br/>\\[ \\begin{eqnarray*} \\simplify[std,!otherNumbers]{{a}*({a3} + {b3} * i + {c3} * i ^ 2 + {d3} * i ^ 3)}&amp;=&amp;\\simplify[std]{{a}*{a3 + b3 * i + c3 * i ^ 2 + d3 * i ^ 3}}\\\\ &amp;=&amp;\\simplify[std]{{a*(a3 + b3 * i + c3 * i ^ 2 + d3 * i ^ 3)}} \\end{eqnarray*} \\]<br/>d)</p>\n  <p>This can be calculated by using the formula twice, firstly to multiply out the first two sets of parentheses,&nbsp;</p>\n  <p>and then to multiply the result of that calculation by the third set of parentheses.</p>\n  <p>So we obtain:<br/>\\[ \\begin{eqnarray*} (\\var{a})(\\var{z1})(\\var{z3})&amp;=&amp;((\\var{a})(\\var{z1}))(\\var{z3})\\\\ &amp;=&amp;(\\var{a*(z1)})(\\var{z3})\\\\ &amp;=&amp;\\var{a*(z1)*(z3)} \\end{eqnarray*} \\]</p>", "extensions": [], "tags": [], "type": "question", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Luis Hernandez", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2870/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Luis Hernandez", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2870/"}]}