{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"math","formal_name":"MATH","introduction":"MATH organises 12,500 high-school competition problems into seven subjects and five difficulty levels, each with a full worked solution. It underlies much of the later mathematics evaluation work; this catalogue imports the full test split: 5,000 problems across all seven subjects.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://github.com/hendrycks/math","indexing_mode":"index","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[],"history":"","construction":"","limitations":"","saturation":"","scores":[]}},"task_id":"fa2ee8c2-c607-5af8-953e-839cfb500e2d","task_key":"precalculus--test--fa2ee8c2-c607-5af8-953e-839cfb500e2d","task_revision_id":"1","upstream_id":"","short_description":"Let $z = 2 + \\sqrt{2} - (3 + 3 \\sqrt{2})i$, and let $c = 2 - 3i$. Let $w$ be the…","config":"precalculus","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Let $z = 2 + \\\\sqrt{2} - (3 + 3 \\\\sqrt{2})i$, and let $c = 2 - 3i$.  Let $w$ be the result when $z$ is rotated around $c$ by $\\\\frac{\\\\pi}{4}$ counter-clockwise.\\n\\n[asy]\\nunitsize(0.6 cm);\\n\\npair C, W, Z;\\n\\nZ = (2 + sqrt(2), -3 - 3*sqrt(2));\\nC = (2,-3);\\nW = rotate(45,C)*(Z);\\n\\ndraw(Z--C--W);\\n\\ndot(\\\"$c$\\\", C, N);\\ndot(\\\"$w$\\\", W, SE);\\ndot(\\\"$z$\\\", Z, S);\\nlabel(\\\"$\\\\frac{\\\\pi}{4}$\\\", C + (0.6,-1));\\n[/asy]\\n\\nFind $w.$\",\"type\":\"Precalculus\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}