// Numbas version: exam_results_page_options
{"name": "Resuelve las operaciones de n\u00fameros complejos y expresa en la forma $ a + bi \\; $ donde $ a $ y $ b $ son reales.", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Resuelve las operaciones de n\u00fameros complejos y expresa en la forma $ a + bi \\; $ donde $ a $ y $ b $ son reales.", "tags": [], "metadata": {"description": "<p>Multiplicaci&oacute;n y suma de n&uacute;meros complejos.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Resuelve las operaciones de n&uacute;meros complejos y expresa en la forma $ a + bi \\; $ donde $ a $ y $ b $ son reales.</p>\n<p>Ingresa todos los n&uacute;meros como fracciones o enteros.&nbsp;No incluya corchetes en su respuesta. Recuerda que $i^2=-1$</p>", "advice": "<p>a)</p>\n<p>La soluci&oacute;n est&aacute; dada por:</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>Esto se puede calcular usando la f&oacute;rmula dos veces, primero para multiplicar los dos primeros conjuntos de par&eacute;ntesis,</p>\n<p>y luego multiplicar el resultado de ese c&aacute;lculo por el tercer conjunto de par&eacute;ntesis.</p>\n<p></p>\n<p>Asi obtenemos:<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>", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "extensions": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "s1*random(1..9)+s2*random(1..9)*i", "description": "", "templateType": "anything"}, "d6": {"name": "d6", "group": "Ungrouped variables", "definition": "s4*random(1..9)", "description": "", "templateType": "anything"}, "s5": {"name": "s5", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "templateType": "anything"}, "s1": {"name": "s1", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "templateType": "anything"}, "c3": {"name": "c3", "group": "Ungrouped variables", "definition": "s3*random(1..9)", "description": "", "templateType": "anything"}, "s4": {"name": "s4", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "templateType": "anything"}, "s2": {"name": "s2", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "templateType": "anything"}, "b3": {"name": "b3", "group": "Ungrouped variables", "definition": "s2*random(1..9)", "description": "", "templateType": "anything"}, "a3": {"name": "a3", "group": "Ungrouped variables", "definition": "s1*random(1..9)", "description": "", "templateType": "anything"}, "f6": {"name": "f6", "group": "Ungrouped variables", "definition": "s6*random(1..9)", "description": "", "templateType": "anything"}, "e6": {"name": "e6", "group": "Ungrouped variables", "definition": "s5*random(3..9)", "description": "", "templateType": "anything"}, "d3": {"name": "d3", "group": "Ungrouped variables", "definition": "s4*random(1..9)", "description": "", "templateType": "anything"}, "z4": {"name": "z4", "group": "Ungrouped variables", "definition": "s6*s2*random(1..9)+s3*s5*random(1..9)*i", "description": "", "templateType": "anything"}, "s3": {"name": "s3", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "templateType": "anything"}, "s6": {"name": "s6", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "templateType": "anything"}, "z3": {"name": "z3", "group": "Ungrouped variables", "definition": "s6*random(1..9)+e6*i", "description": "", "templateType": "anything"}, "z1": {"name": "z1", "group": "Ungrouped variables", "definition": "s3*random(1..9)+f6*i", "description": "", "templateType": "anything"}, "z2": {"name": "z2", "group": "Ungrouped variables", "definition": "s2*random(1..9)+d6*i", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "f6", "s3", "s2", "s1", "d3", "s6", "s5", "s4", "c3", "a3", "b3", "d6", "e6", "z4", "z1", "z2", "z3"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\var{e6*i}(\\simplify[std]{{a}})\\;=\\;$[[0]].</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{a*e6*i}", "answerSimplification": "std", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": 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Also do not include brackets in your answers.</p>"}, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$(\\simplify[std]{{a}})(\\simplify[std]{{z4}})\\;=\\;$[[0]].</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "({a*z4})", "answerSimplification": "std", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "notallowed": {"strings": [".", ")", "("], "showStrings": false, "partialCredit": 0, "message": "<p>Input all numbers as fractions or integers. 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