Find series representations for all indicated regions. a. (f(z)=frac{z}{z-1},|z| <1,|z|>1). b. (f(z)=frac{1}{(z-i)(z+2)},|z| <1,1 2). [Hint: Use partial

Find series representations for all indicated regions.

a. \(f(z)=\frac{z}{z-1},|z|<1,|z|>1\).

b. \(f(z)=\frac{1}{(z-i)(z+2)},|z|<1,1<|z|<2,|z|>2\). [Hint: Use partial fractions to write this as a sum of two functions first.]