// Numbas version: exam_results_page_options
{"name": "Hyperbolic 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": [{"variable_groups": [], "variables": {"b1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..9)", "description": "", "name": "b1"}, "c1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(0..1 except a1)", "description": "", "name": "c1"}, "a1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(0,1)", "description": "", "name": "a1"}, "d1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..9)", "description": "", "name": "d1"}}, "ungrouped_variables": ["a1", "c1", "b1", "d1"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Hyperbolic function in real-imaginary form", "functions": {}, "showQuestionGroupNames": false, "parts": [{"scripts": {}, "gaps": [{"answer": "{a1}*sinh({b1}*x)*cos({b1}*y)+{c1}*cosh({d1}*x)*cos({d1}*y)", "vsetrange": [0, 1], "checkingaccuracy": 0.001, "checkvariablenames": true, "expectedvariablenames": ["x", "y"], "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "type": "jme", "showCorrectAnswer": true, "marks": 1, "vsetrangepoints": 5}, {"answer": "{a1}*cosh({b1}*x)*sin({b1}*y)+{c1}*sinh({d1}*x)*sin({d1}*y)", "vsetrange": [0, 1], "checkingaccuracy": 0.001, "checkvariablenames": true, "expectedvariablenames": ["x", "y"], "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "type": "jme", "showCorrectAnswer": true, "marks": 1, "vsetrangepoints": 5}], "type": "gapfill", "prompt": "\n<p>$g(x,y)=$ [[0]].</p>\n  <p>$h(x,y)=$ [[1]].</p>\n", "showCorrectAnswer": true, "marks": 0}], "statement": "<p>Express the function $f(z)=\\simplify{{a1}*sinh({b1}*z)+{c1}*cosh({d1}*z)}$ in real-imaginary form $f(z)=g(x,y)+ih(x,y)$, given that $z=x+iy$.</p>", "tags": ["MAS2103", "checked2015"], "rulesets": {}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"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>", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Express $f(z)$ in real-imaginary form, given that $z=x+iy$, where $f(z)$ involves hyperbolic functions.</p>"}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "<p>Substitute $z=x+iy$ into the expression for $f(z)$, so that</p>\n<p>\\[f(z)=f(x+iy)=\\simplify{{a1}*sinh({b1}*(x+iy))+{c1}*cosh({d1}*(x+iy))},\\]</p>\n<p>then use the identity</p>\n<p>\\[\\simplify{{a1}*sinh(u+i*v)+{c1}*cosh(u+i*v)}=\\simplify{{a1}*(sinh(u)*cos(v)+i*cosh(u)*sin(v))+{c1}*(cosh(u)*cos(v)+i*sinh(u)*sin(v))},\\]</p>\n<p>and rearrange to give</p>\n<p>\\[f(z)=\\simplify{{a1}*sinh({b1}*x)*cos({b1}*y)+{a1}*i*cosh({b1}*x)*sin({b1}*y)+{c1}*cosh({d1}*x)*cos({d1}*y)+{c1}*i*sinh({d1}*x)*sin({d1}*y)}.\\]</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/"}]}