{"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":"315c4f83-0ad5-55dd-9fc3-6c9f54b6463a","task_key":"precalculus--test--315c4f83-0ad5-55dd-9fc3-6c9f54b6463a","task_revision_id":"1","upstream_id":"","short_description":"A sequence $(z_n)$ of complex numbers satisfies the following properties:","config":"precalculus","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"A sequence $(z_n)$ of complex numbers satisfies the following properties:\\n\\n$z_1$ and $z_2$ are not real.\\n$z_{n+2}=z_{n+1}^2z_n$ for all integers $n\\\\geq 1$.\\n$\\\\dfrac{z_{n+3}}{z_n^2}$ is real for all integers $n\\\\geq 1$.\\n$\\\\left|\\\\dfrac{z_3}{z_4}\\\\right|=\\\\left|\\\\dfrac{z_4}{z_5}\\\\right|=2$.\\n\\nFind the product of all possible values of $z_1$.\",\"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":[]}