// Numbas version: exam_results_page_options
{"name": "Contour integral of a complex function", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "variables": {"b1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..5)", "description": "", "name": "b1"}, "a1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(0..5)", "description": "", "name": "a1"}}, "ungrouped_variables": ["a1", "b1"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Contour integral of a complex function", "functions": {}, "showQuestionGroupNames": false, "parts": [{"scripts": {}, "gaps": [{"answer": "-({a1^3}+i*{b1^3})/3", "vsetrange": [0, 1], "checkingaccuracy": 0.001, "checkvariablenames": false, "expectedvariablenames": [], "notallowed": {"message": "<p>Do not enter decimals in your answer.</p>", "showStrings": false, "partialCredit": 0, "strings": ["."]}, "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "type": "jme", "showCorrectAnswer": true, "marks": 1, "vsetrangepoints": 5}], "type": "gapfill", "prompt": "<p>$I=$ [[0]]. &nbsp;(Do not enter decimals in your answer.)</p>", "showCorrectAnswer": true, "marks": 0}], "statement": "<p>Find the value of the integral</p>\n    <p>\\[I=\\int_C{\\!z^2\\,\\mathrm{d}z},\\]</p>\n    <p>along any path $C$ from $z=\\var{a1}$ to $z=\\simplify{{b1}*i}$.</p>", "tags": ["checked2015", "MAS2103"], "rulesets": {}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "<p><strong>15/7/2012:</strong></p>\n<p>Added tags.</p>", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Contour integral of $z^2$ along any path.</p>"}, "variablesTest": {"condition": "b1=1", "maxRuns": 100}, "advice": "<p>This is an exercise in integration, so</p>\n    <p>\\[\\begin{align}I&amp;=\\int_C{\\!z^2\\,\\mathrm{d}z}\\\\&amp;=\\int_{\\var{a1}}^{\\simplify{{b1}*i}}{\\!z^2\\,\\mathrm{d}z}\\\\&amp;=\\left[\\frac{1}{3}z^3\\right]_{\\var{a1}}^{\\simplify{{b1}*i}}\\\\&amp;=\\frac{1}{3}\\left(\\simplify{{b1^3}*i^3}-\\var{a1}^3\\right)\\\\&amp;=-\\frac{1}{3}\\left(\\simplify{{a1^3}+{b1^3}*i}\\right).\\end{align}\\]</p>", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}