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