// Numbas version: exam_results_page_options
{"name": "Hollie's copy of Function in real-imaginary form", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"question_groups": [{"pickingStrategy": "all-ordered", "name": "", "questions": [], "pickQuestions": 0}], "ungrouped_variables": ["a1", "n2", "n3", "b1", "n"], "variables": {"a1": {"description": "", "templateType": "anything", "name": "a1", "group": "Ungrouped variables", "definition": "random(1..5)"}, "n2": {"description": "", "templateType": "anything", "name": "n2", "group": "Ungrouped variables", "definition": "switch (\n  n=2, 1,\n  n=3, 0\n)"}, "n3": {"description": "", "templateType": "anything", "name": "n3", "group": "Ungrouped variables", "definition": "switch (\n  n=2, 0,\n  n=3, 1\n)"}, "b1": {"description": "", "templateType": "anything", "name": "b1", "group": "Ungrouped variables", "definition": "random(1..5 except a1)"}, "n": {"description": "", "templateType": "anything", "name": "n", "group": "Ungrouped variables", "definition": "random(2,3)"}}, "preamble": {"js": "", "css": ""}, "tags": ["MAS2103", "checked2015"], "type": "question", "advice": "<p>All that is required in this question is to substitute $z=x+iy$ into the expression for $f(z)$, and rearrange to the form $f(z)=g(x,y)+ih(x,y)$, hence</p>\n<p>\\[\\begin{align}f(z)&amp;=f(x+iy)\\\\&amp;=\\simplify{{a1}*(x+iy)^{n}-i*{b1}*(x+iy)^{n-1}}\\\\&amp;=\\simplify{{n2}*({a1}*(x^2-y^2)+{b1}*y) + {n3}*({a1}*(x^3-3*x*y^2)+{2*b1}*x*y)+i*({n2}*({2*a1}*x*y-{b1}*x)+{n3}*({3*a1}*x^2*y-{a1}*y^3-{b1}*(x^2+y^2)))}.\\end{align}\\]</p>", "name": "Hollie's copy of Function in real-imaginary form", "variablesTest": {"maxRuns": 100, "condition": ""}, "parts": [{"gaps": [{"answer": "{n2}*({a1}*(x^2-y^2)+{b1}*y) + {n3}*({a1}*(x^3-3*x*y^2)+{2*b1}*x*y)", "showCorrectAnswer": true, "showpreview": true, "expectedvariablenames": ["x", "y"], "type": "jme", "checkingtype": "absdiff", "answersimplification": "std", "marks": 1, "vsetrange": [0, 1], "checkingaccuracy": 0.001, "checkvariablenames": true, "vsetrangepoints": 5, "scripts": {}}, {"answer": "{n2}*({2*a1}*x*y-{b1}*x)+{n3}*({3*a1}*x^2*y-{a1}*y^3-{b1}*(x^2-y^2))", "showCorrectAnswer": true, "showpreview": true, "expectedvariablenames": ["x", "y"], "type": "jme", "checkingtype": "absdiff", "answersimplification": "std", "marks": 1, "vsetrange": [0, 1], "checkingaccuracy": 0.001, "checkvariablenames": true, "vsetrangepoints": 5, "scripts": {}}], "showCorrectAnswer": true, "prompt": "<p>$g(x,y)=$ [[0]].</p>\n<p>$h(x,y)=$ [[1]].</p>", "type": "gapfill", "marks": 0, "scripts": {}}], "variable_groups": [], "metadata": {"description": "<p>Express $f(z)$ in real-imaginary form, given that $z=x+iy$.</p>", "notes": "<p><strong>15/7/2012:</strong></p>\n<p>Added tags.</p>\n<p><strong>25/02/2014</strong></p>\n<p>Enable unexpected variable names. AJY</p>\n<p><strong>17/02/2014</strong></p>\n<p>Fix typo in solution to $h(x,y)$. AJY</p>", "licence": "Creative Commons Attribution 4.0 International"}, "functions": {}, "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "showQuestionGroupNames": false, "statement": "<p>Express the function $f(z)=\\simplify{{a1}*z^{n}-i*{b1}*z^{n-1}}$ in real-imaginary form $f(z)=g(x,y)+ih(x,y)$, given that $z=x+iy$.</p>", "contributors": [{"name": "Hollie Tarr", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1176/"}]}]}], "contributors": [{"name": "Hollie Tarr", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1176/"}]}