lean_workbook_plus_30282

Let $x, \; y, \; z \in \mathbb{C}$ . We can use the following factorization: $x^3 + y^3 + z^3 - 3xyz = (x + y + z)(x^2 + y^2 + z^2 - xy - yz - zx)$ . If $x + y + z = 0$ , prove that $x^3 + y^3 + z^3 = 3xyz$ .