High Quality Content by WIKIPEDIA articles! There are n different nth roots of unity: zk (k = 1, 2, 3, ..., n) where z is any primitive nth root of unity. These n roots are distributed evenly over the unit circle as can be seen in the plot on the right-hand side of the three 3rd roots of unity. There are ?(n) primitive nth roots of unity. If z is any fixed primitive nth root of unity, then the primitive nth roots of unity are those zk where 1 ? k ? n and k and n are coprime. The notion of root of unity also applies to any algebraic ring with 1, namely a root of unity is any element of finite multiplicative order.

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