Holomorphic Function

Hello,
Two links below one is the problem sheet and one is the solution sheet.

I'm stuck on question 3 . There are two parts of the solution I don't quite understand.

The very first line

z^n-z(0)^n= that expansion. How did he get this?

and also a little bit further down where he states that the

co-efficient of z^-1 on RHS is ... I cant seem to get what he gets correctly.

Thanks a lot.

Got a big exam on monday so any help is appreciated.

Problem Sheet

Solutions