This is complex variable. I am returning student, so in detailed explanation please. Thank you.

Problem 4. Prove the following: (a) If f is analytic at zo, then f has a pole of order k at zo if and only if f can be written as f ( 2 ) = (2 -20)* g(2) . where g (z) is analytic at zo at g (20) # 0. (b) If f is analytic on 0