Mathegoras

Complex numbers › Roots of unity and complex roots › Counting complex solutions

Imaginary part of a complex root pair

High school · ●●●○○ 50 pts

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

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roots of unity