benchmarks.wiki / Public workspace
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Omni-MATH / During the weekends, Eli delivers milk in the complex plane. On Saturday, he…
Problem
Answer published by the source. Consult the official source to check your work against its answer.
problem
During the weekends, Eli delivers milk in the complex plane. On Saturday, he begins at and delivers milk to houses located at , in that order; on Sunday, he begins at 1 and delivers milk to houses located at , in that order. Eli always walks directly (in a straight line) between two houses. If the distance he must travel from his starting point to the last house is on both days, find the real part of .
Plain-text mathematical notation (without MathML)
During the weekends, Eli delivers milk in the complex plane. On Saturday, he begins at z and delivers milk to houses located at z³,z⁵,z⁷,…,z²⁰¹³, in that order; on Sunday, he begins at 1 and delivers milk to houses located at z²,z⁴,z⁶,…,z²⁰¹², in that order. Eli always walks directly (in a straight line) between two houses. If the distance he must travel from his starting point to the last house is √(2012) on both days, find the real part of z².
Original LaTeX notation
During the weekends, Eli delivers milk in the complex plane. On Saturday, he begins at $z$ and delivers milk to houses located at $z^{3}, z^{5}, z^{7}, \ldots, z^{2013}$, in that order; on Sunday, he begins at 1 and delivers milk to houses located at $z^{2}, z^{4}, z^{6}, \ldots, z^{2012}$, in that order. Eli always walks directly (in a straight line) between two houses. If the distance he must travel from his starting point to the last house is $\sqrt{2012}$ on both days, find the real part of $z^{2}$.Discussion
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Source and history
- task_id
479abed3-3271-520f-87d4-1eada6b19f32- task_key
test--479abed3-3271-520f-87d4-1eada6b19f32- task_revision_id
- 1
- config / split
- / test
initial import