[SOLVED] Complex Taylor, Maclaurin and Laurent series

**1)** Find the Taylor series around the point 2i and specify the radius of convergence:

(a)

(b)

(a): and where

So the Taylor series is:

My textbook has a slightly different answer though. And the radius of convergence? Do I need to use the ratio test, or is there some simpler way to deal with it?

**2) **Find the first three nonvanishing terms for the Maclaurin series of:

**3)** Determine the Laurent series for ,

I've solved this for different areas, but I'm having a little trouble with this one.