Consider the function f: C -> C defined by
∀ x, y ∈ R, f(x + iy) = y^3 - 3y + 1 - ix^3.
Question 1 (3 points): Prove that, for every z ∈ C, the function f is C-differentiable at z if and only if |z| = 1. Moreover, prove that f(z) = -3iRz for all z ∈ C such that |z| = 1.