other names: nth root of unity, kth root of unity
    complex analysis:
    If n `>=` 1 is an integer, then an nth root of unity is a complex number `zeta ` with `zeta^n` = 1.
    
    If complex number lie on the unit circle then the polar coordinates of (`ninNN, theta = (2 pi)/n, zeta = e^(itheta)`):
    `zeta^4` = 1 are `(1, 4theta)`, `theta = (4pi)/8 = pi/2`: (1, 1), (1, i), (1, -1), (1, -i)
    
    `zeta^n` = 1 are `(1, ntheta)` = (1, 0), because the nth roots of unity are equally spaced around the unit circle.