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Imaginary part of a complex number

Source: 2012 AIME I Problem 6

March 16, 2012
trigonometryAMCAIMEconicsparabolaLaTeXcomplex numbers

Problem Statement

The complex numbers zz and ww satisfy z13=wz^{13} = w, w11=zw^{11} = z, and the imaginary part of zz is sin⁡(mπn)\sin\left(\frac{m\pi}n\right) for relatively prime positive integers mm and nn with m<nm < n. Find nn.
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