Let x be the cube root of unity, then
x = (1)1/3
x3 = 1
(x − 1)(x2 + x + 1) = 0
x − 1 = 0 and x2 + x + 1 = 0
Cube roots of unity are
The two complex roots are conjugate to each other.
In an equation with real coefficients, imaginary roots occur in pairs (one root is the conjugate of the other).
Theorem: For any polynomial equation P(x) = 0 with real coefficients, imaginary (complex) roots occur in conjugate pairs.