Prove:

1. Show that if f(z) has a zero of order n>1 at z=z 0. then f'(z) has a zero of order n-1 at z0

2. Prove: Let f(z) be analytic at z=z0 and have a zero of nth order at z=z0. Then 1/f(z) has a pole of nth order at z=z0; and so does h(z)/f(z), provided h(z) is analytic at z=z0 and h(z0) is not equal to 0.