A root of unity is a complex number that when raised to some positive integer will return 1.
It is any complex number z which satisfies the following equation:
z^n = 1
where n in NN, which is to say that n is a natural number. A natural number is any positive integer: (n = 1, 2, 3, ...). This is sometimes referred to as a counting number and the notation for it is NN.
For any n, there may be multiple z values that satisfy that equation, and those values comprise the roots of unity for that n.
When n = 1
Roots of unity: 1
When n = 2
Roots of unity: -1, 1
When n = 3
Roots of unity = 1, (1 + sqrt(3)i)/2, (1 - sqrt(3)i)/2
When n = 4
Roots of unity = -1, i, 1, -i
