2012 AIME I Problems/Problem 6

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Problem 6

Let $z$ and $w$ be complex numbers such that $z^{13} = w$ and $w^{11} = z$. If the imaginary part of $z$ can be written as $\sin {\frac{m\pi}{n}}$, where $m$ and $n$ are relatively prime positive integers, find $n$.

See also

2012 AIME I (ProblemsAnswer KeyResources)
Preceded by
Problem 5
Followed by
Problem 7
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All AIME Problems and Solutions
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