// Numbas version: exam_results_page_options
{"name": "Grainne's copy of Amit'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": [{"variables": {"e6": {"description": "", "definition": "s5*random(3..9)", "name": "e6", "group": "Ungrouped variables", "templateType": "anything"}, "z3": {"description": "", "definition": "s6*random(1..9)+e6*i", "name": "z3", "group": "Ungrouped variables", "templateType": "anything"}, "f6": {"description": "", "definition": "s6*random(1..9)", "name": "f6", "group": "Ungrouped variables", "templateType": "anything"}, "a": {"description": "", "definition": "s1*random(1..9)+s2*random(1..9)*i", "name": "a", "group": "Ungrouped variables", "templateType": "anything"}, "a3": {"description": "", "definition": "s1*random(1..9)", "name": "a3", "group": "Ungrouped variables", "templateType": "anything"}, "s4": {"description": "", "definition": "random(1,-1)", "name": "s4", "group": "Ungrouped variables", "templateType": "anything"}, "c3": {"description": "", "definition": "s3*random(1..9)", "name": "c3", "group": "Ungrouped variables", "templateType": "anything"}, "z2": {"description": "", "definition": "s2*random(1..9)+d6*i", "name": "z2", "group": "Ungrouped variables", "templateType": "anything"}, "s5": {"description": "", "definition": "random(1,-1)", "name": "s5", "group": "Ungrouped variables", "templateType": "anything"}, "d3": {"description": "", "definition": "s4*random(1..9)", "name": "d3", "group": "Ungrouped variables", "templateType": "anything"}, "s6": {"description": "", "definition": "random(1,-1)", "name": "s6", "group": "Ungrouped variables", "templateType": "anything"}, "s3": {"description": "", "definition": "random(1,-1)", "name": "s3", "group": "Ungrouped variables", "templateType": "anything"}, "d6": {"description": "", "definition": "s4*random(1..9)", "name": "d6", "group": "Ungrouped variables", "templateType": "anything"}, "z4": {"description": "", "definition": "s6*s2*random(1..9)+s3*s5*random(1..9)*i", "name": "z4", "group": "Ungrouped variables", "templateType": "anything"}, "s2": {"description": "", "definition": "random(1,-1)", "name": "s2", "group": "Ungrouped variables", "templateType": "anything"}, "s1": {"description": "", "definition": "random(1,-1)", "name": "s1", "group": "Ungrouped variables", "templateType": "anything"}, "b3": {"description": "", "definition": "s2*random(1..9)", "name": "b3", "group": "Ungrouped variables", "templateType": "anything"}, "z1": {"description": "", "definition": "s3*random(1..9)+f6*i", "name": "z1", "group": "Ungrouped variables", "templateType": "anything"}}, "functions": {}, "name": "Grainne's copy of Amit's copy of Arithmetics of complex numbers II", "variablesTest": {"maxRuns": 100, "condition": ""}, "type": "question", "variable_groups": [], "preamble": {"js": "", "css": ""}, "ungrouped_variables": ["a", "f6", "s3", "s2", "s1", "d3", "s6", "s5", "s4", "c3", "a3", "b3", "d6", "e6", "z4", "z1", "z2", "z3"], "showQuestionGroupNames": false, "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Multiplication and addition of complex numbers. Four parts.</p>", "notes": "<p><strong>15/07/2015:</strong></p>\n<p>Added tags.</p>\n<p><strong>4/7/2012</strong></p>\n<p>Added tags</p>\n<p><span id=\"prompt\"><span><span id=\"MathJax-Element-42-Frame\" class=\"MathJax\"><span id=\"MathJax-Span-1241\" class=\"math\"><strong>Same problem in Complex Numbers_2. </strong></span></span></span></span><strong>Question a</strong> - sometimes the complex number is generated as a/(b+i*c) but sometimes the complex number is displayed as a decimal, i.e. <span id=\"prompt\"><span><span id=\"MathJax-Element-42-Frame\" class=\"MathJax\"><span id=\"MathJax-Span-1241\" class=\"math\">0.0975609756+0.1219512195i if this happens then the question is invalid. This is an issue on github.<br /></span></span></span></span></p>\n<p><span><span><span class=\"MathJax\"><span class=\"math\"><strong>16/07/2012:</strong><br /></span></span></span></span></p>\n<p><span><span><span class=\"MathJax\"><span class=\"math\">Issue above resolved. Also forbid decimals and brackets. Questions cannot now be answered by simply repeating the expression.</span></span></span></span></p>\n<p><span><span><span class=\"MathJax\"><span class=\"math\">Added formal cba name&nbsp;</span></span></span></span>mas104220122013CBA1_3&nbsp;as a tag</p>"}, "tags": ["addition of complex numbers", "algebra of complex numbers", "checked2015", "complex numbers", "mas1602", "MAS1602", "multiplication of complex numbers"], "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>", "question_groups": [{"pickingStrategy": "all-ordered", "name": "", "pickQuestions": 0, "questions": []}], "parts": [{"scripts": {}, "variableReplacements": [], "marks": 0, "type": "gapfill", "variableReplacementStrategy": "originalfirst", "gaps": [{"checkingtype": "absdiff", "scripts": {}, "type": "jme", "marks": 1, "expectedvariablenames": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "notallowed": {"strings": [".", ")", "("], "partialCredit": 0, "message": "<p>Input all numbers as fractions or integers. Also do not include brackets in your answers.</p>", "showStrings": false}, "answersimplification": "std", "vsetrange": [0, 1], "checkvariablenames": false, "variableReplacements": [], "showpreview": true, "answer": "{a*e6*i}", "vsetrangepoints": 5, "checkingaccuracy": 0.001}], "prompt": "<p>$\\var{e6*i}(\\simplify[std]{{a}})\\;=\\;$[[0]].</p>", "showCorrectAnswer": true}, {"scripts": {}, "variableReplacements": [], "marks": 0, "type": "gapfill", "variableReplacementStrategy": "originalfirst", "gaps": [{"checkingtype": "absdiff", "scripts": {}, "type": "jme", "marks": 1, "expectedvariablenames": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "notallowed": {"strings": [".", ")", "("], "partialCredit": 0, "message": "<p>Input all numbers as fractions or integers. Also do not include brackets in your answers.</p>", "showStrings": false}, "answersimplification": "std", "vsetrange": [0, 1], "checkvariablenames": false, "variableReplacements": [], "showpreview": true, "answer": "({a*z4})", "vsetrangepoints": 5, "checkingaccuracy": 0.001}], "prompt": "<p>$(\\simplify[std]{{a}})(\\simplify[std]{{z4}})\\;=\\;$[[0]].</p>", "showCorrectAnswer": true}, {"scripts": {}, "variableReplacements": [], "marks": 0, "type": "gapfill", "variableReplacementStrategy": "originalfirst", "gaps": [{"checkingtype": "absdiff", "scripts": {}, "type": "jme", "marks": 1, "expectedvariablenames": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "notallowed": {"strings": [".", ")", "("], "partialCredit": 0, "message": "<p>Input all numbers as fractions or integers. Also do not include brackets in your answers.</p>", "showStrings": false}, "vsetrange": [0, 1], "checkvariablenames": false, "variableReplacements": [], "showpreview": true, "answer": "{(a3 + b3 * i + c3 * i ^ 2 + d3 * i ^ 3)*a}", "vsetrangepoints": 5, "checkingaccuracy": 0.001}], "prompt": "<p>$\\simplify[std,!otherNumbers]{{a}*({a3} + {b3} * i + {c3} * i ^ 2 + {d3} * i ^ 3)}\\;=\\;$[[0]].</p>", "showCorrectAnswer": true}, {"scripts": {}, "variableReplacements": [], "marks": 0, "type": "gapfill", "variableReplacementStrategy": "originalfirst", "gaps": [{"checkingtype": "absdiff", "scripts": {}, "type": "jme", "marks": 1, "expectedvariablenames": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "notallowed": {"strings": [".", ")", "("], "partialCredit": 0, "message": "<p>Input all numbers as fractions or integers. Also do not include brackets in your answers.</p>", "showStrings": false}, "vsetrange": [0, 1], "checkvariablenames": false, "variableReplacements": [], "showpreview": true, "answer": "{a*(z1)*(z3)}", "vsetrangepoints": 5, "checkingaccuracy": 0.001}], "prompt": "<p>$(\\simplify[std]{{a}})(\\simplify[std]{ {z1}})(\\simplify[std]{ {z3}})\\;=\\;$[[0]].</p>", "showCorrectAnswer": true}], "statement": "<p>Find the following complex numbers in the form $a+bi\\;$ where $a$ and $b$ are real.</p>\n    <p>Input all numbers as fractions or integers. Also do not include brackets in your answers.</p>", "contributors": [{"name": "Grainne Scanlon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2165/"}]}]}], "contributors": [{"name": "Grainne Scanlon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2165/"}]}