If x, y and z are the cube roots of unity, then what is the value of xy + yz + zx?

The cube roots of unity are 1, ω, ω² which satisfy 1 + ω + ω² = 0 and 1·ω·ω² = 1. By Vieta's formulas for z³ − 1 = 0, the sum of products taken two at a time equals the coefficient of z (which is 0). So xy + yz + zx = 0.