(a) Show that if f(z) has a zero of order n > 1 at z = z₀, then f'(z) has a zero of order n - 1 at z₀.

(b) Poles and zeros. Prove Theorem 4.

(c) Show that the points at which a nonconstant analytic function f(z) has a given value k are isolated.

(d) If f₁(z) and f₂(z) are analytic in a domain D and equal at a sequence of points z_n in D that converges in D, show that f₁(z) = f₂(z) in D.