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AMC (AIMO validation set) / https://artofproblemsolving.com/wiki/index.php/2023_AMC_12A_Problems/Problem_14 / How many complex numbers satisfy the equation z⁵=(z)¯, where (z)¯ is the conjugate of the complex number z?

Problem

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problem

How many complex numbers satisfy the equation

z^5=\overline{z}

, where

\overline{z}

is the conjugate of the complex number

z

Plain-text mathematical notation (without MathML)

How many complex numbers satisfy the equation z⁵=(z)¯, where (z)¯ is the conjugate of the complex number z?

Original LaTeX notation

How many complex numbers satisfy the equation $z^5=\overline{z}$, where $\overline{z}$ is the conjugate of the complex number $z$?

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Source and history

upstream_id / Original problem ID: https://artofproblemsolving.com/wiki/index.php/2023_AMC_12A_Problems/Problem_14
task_id: d94b256d-1e0d-53e1-a386-e643d5f64f5a
task_key: default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2023~5fAMC~5f12A~5fProblems~2fProblem~5f14
task_revision_id: 2
config / split: default / train

Official source

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