1. Prove that f(2)= 2³ is an entire function, and show that f'(2) = 32². 2. (a) Prove the product rule for complex functions. More specifically, if f(2) and g(2) are analytic prove that h() = f(z)g() is also analytic, and that h'(z) = f'(a)g() + f(z)g (2). (You may use results from the multivariable part of the course without proof.) (b) Let S,, be the statement "n"-1 for n € N = {1,2,3,...}. dz Your textbook establishes that S₁ is true. With the help of (a), show that if S₁, is true, then Sn+1 is true. Why does this establish that S,, is true for all n € N?