// Numbas version: exam_results_page_options
{"name": "Resuelve las operaciones indicadas y exprese el resultado en la forma $a+bi$", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Resuelve las operaciones indicadas y exprese el resultado en la forma $a+bi$", "tags": [], "metadata": {"description": "<p>Multiplicaci&oacute;n y divisi&oacute;n de n&uacute;meros complejos.&nbsp;</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<div class=\"tlid-input input\">\n<div class=\"source-wrap\">\n<div class=\"input-full-height-wrapper tlid-input-full-height-wrapper\">\n<div class=\"source-input\">\n<div class=\"source-header\">\n<div class=\"go-wrap\">Resuelve las operaciones de n&uacute;meros complejos&nbsp; y exprese el resultado en la forma $a+bi$</div>\n</div>\n<div class=\"source-footer-wrap source-or-target-footer\">\n<div class=\"source-footer\">\n<div class=\"speech-wrap source-or-target-footer-button left-positioned\">\n<div id=\"gt-speech\" class=\"speech-button goog-toolbar-button\" aria-label=\"Activar la entrada de voz\" data-tooltip-align=\"t,c\" aria-pressed=\"false\" role=\"button\" aria-disabled=\"false\" data-tooltip=\"Activar la entrada de voz\" tabindex=\"0\"><span title=\"\" class=\"\">Ingrese $ a $ y $ b $ como fracciones y no como decimales.</span> <span title=\"\" class=\"\">Tampoco incluya corchetes en su respuesta.</span></div>\n</div>\n</div>\n</div>\n</div>\n</div>\n</div>\n</div>\n<p>.</p>", "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  ", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "extensions": [], "variables": {"rz3": {"name": "rz3", "group": "Ungrouped variables", "definition": "if(a3=re(z1),a3+random(1,-1),a3)", "description": "", "templateType": "anything"}, "z1": {"name": "z1", "group": "Ungrouped variables", "definition": "s2*random(1..9)+s1*random(1..9)*i", "description": "", "templateType": "anything"}, "z3": {"name": "z3", "group": "Ungrouped variables", "definition": "rz3+s1*random(1..9)*i", "description": "", "templateType": "anything"}, "s2": {"name": "s2", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "templateType": "anything"}, "s4": {"name": "s4", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "templateType": "anything"}, "c1": {"name": "c1", "group": "Ungrouped variables", "definition": "s3*random(1..9)", "description": "", "templateType": "anything"}, "s3": {"name": "s3", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "templateType": "anything"}, "z2": {"name": "z2", "group": "Ungrouped variables", "definition": "re(z1)+s2*random(1,2)+s4*random(1..9)*i", "description": "", "templateType": "anything"}, "a3": {"name": "a3", "group": "Ungrouped variables", "definition": "s3*random(1..9)", "description": "", "templateType": "anything"}, "c2": {"name": "c2", "group": "Ungrouped variables", "definition": "random(1..5)", "description": "", "templateType": "anything"}, "s1": {"name": "s1", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["s3", "s2", "s1", "s4", "a3", "rz3", "c2", "c1", "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": "\n      <p>\\[\\displaystyle z=\\simplify[!collectNumbers]{({z3}*{z2})/{z1}}\\]</p>\n      <p>$z=\\;\\;$[[0]].</p>\n      ", "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": "{re(conj(z1)*z3*z2)}/{abs(z1)^2}+{im(conj(z1)*z3*z2)}/{abs(z1)^2}*i", "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>Make sure that you input the real and imaginary parts as fractions or integers and not as decimals. Also do not include brackets in your answer.</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": "\n      <p>\\[\\displaystyle z=\\simplify[!collectNumbers]{({z2}*{z1})}(\\var{z3})^{-1}\\]</p>\n      <p>$z=\\;\\;$[[0]].</p>\n      ", "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": "{re(conj(z3)*z1*z2)}/{abs(z3)^2}+{im(conj(z3)*z1*z2)}/{abs(z3)^2}*i", "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>Make sure that you input the real and imaginary parts as fractions or integers and not as decimals. Also do not include brackets in your answer.</p>"}, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "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/"}]}