The nth complex roots of unity are often useful as clever choices for n arbitrary numbers. (Example: FFT)

There are n nth complex roots of unity for any positive integer n. The easiest way to find them is to note that they are given by

cis(2k×pi/n) for k in {1, ..., n}. (Well, really for all positive integers k, but they just repeat after that; {1, ..., n} gives you the n distinct ones.)

An easy way to visualize this is to take the unit circle in the complex plane. To find the nth roots, cut the circle into n even pie pieces. The unit vectors that represent the cuts are the nth roots; there are n of them.

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