{"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":"6772a119-27f5-5d0a-ba9f-34ba18968f99","task_key":"precalculus--test--6772a119-27f5-5d0a-ba9f-34ba18968f99","task_revision_id":"1","upstream_id":"","short_description":"The solutions to $z^4 = 4 - 4i \\sqrt{3}$ can be expressed in the form","config":"precalculus","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"The solutions to $z^4 = 4 - 4i \\\\sqrt{3}$ can be expressed in the form\\n\\\\begin{align*}\\nz_1 &= r_1 (\\\\cos \\\\theta_1 + i \\\\sin \\\\theta_1), \\\\\\\\\\nz_2 &= r_2 (\\\\cos \\\\theta_2 + i \\\\sin \\\\theta_2), \\\\\\\\\\nz_3 &= r_3 (\\\\cos \\\\theta_3 + i \\\\sin \\\\theta_3), \\\\\\\\\\nz_4 &= r_4 (\\\\cos \\\\theta_4 + i \\\\sin \\\\theta_4),\\n\\\\end{align*}where $r_k > 0$ and $0^\\\\circ \\\\le \\\\theta_k < 360^\\\\circ.$  Find $\\\\theta_1 + \\\\theta_2 + \\\\theta_3 + \\\\theta_4,$ in degrees.\",\"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":[]}