Complex z and w satisfy power equations

2050SpecialistComplex NumbersNumber Theory

AIME I · 2012 · Problem 6

The complex numbers $z$ and $w$ satisfy $z^{13} = w,$ $w^{11} = z,$ and the imaginary part of $z$ is $\sin{\frac{m\pi}{n}}$, for relatively prime positive integers $m$ and $n$ with $m<n.$ Find $n.$

0 students attempted0% solvedRating 2050

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Complex z and w satisfy power equations

2050SpecialistComplex NumbersNumber Theory

AIME I · 2012 · Problem 6

The complex numbers $z$ and $w$ satisfy $z^{13} = w,$ $w^{11} = z,$ and the imaginary part of $z$ is $\sin{\frac{m\pi}{n}}$, for relatively prime positive integers $m$ and $n$ with $m<n.$ Find $n.$

0 students attempted0% solvedRating 2050