Find all the cube roots of 1

Let z be a cube root of 1 such that: z^3 = 1 z^3 - 1 = 0 Factorise: (z-1)(z^2 + z + 1) = 0 Then, z=1, the real root, or: z^2 + z + 1 = 0 with z not equal to 1 Use quadratic equation: z = (-1 +- sqrt(1-4))/2 sqrt(1-4)=sqrt(3)i, an imaginary number Tidy up: z = -0.5 +- sqrt(3)i/2