Let f be nonconstant and analytic in the closed disk D1(0). Suppose that ∣f(z)∣ is constant for z∈C1(0), i.e., that there is some number K such that ∣f(z)∣=K for all z∈C1(0). Show that f has a zero in D1(0), i.e., that there exists some z0∈D1(0) such that f(z0)=0. Hint: use both the minimum modulus principle (see Exercise 7) and maximum modulus principle.