Finding the roots of a given equation

Question

How can I show that the three roots of the equation z³ = 1 are:

ω = (-1+ i√(3))/2,

ω² = (-1- i√(3))/2

ω³ = 1

Answer 1

z³ - 1 = 0

(z - 1)(z² + z + 1) = 0

z - 1 = 0, z = 1

or

z² + z + 1 = 0

Solve using Quadratic Formula

Answer 2

z³ - 1 = (z - 1)(z² + z + 1) = 0; z - 1 = 0 z = 1. Or z² + z + 1 = 0; z = (-1 ± √1 - 4)/2 = (-1 ± i√3)/2