# Finding the Power Series of a Complex fuction.

Find a power series expression $\sum_{n=0}^\infty A_n z^n$ for $\frac{1}{z^2-\sqrt2 z +2}$

I'm completely stuck on this question. I know how to manipulate power series but I've never had to find one from such a complicated function. Also we're asked to find the radius of convergence although this I think I can do. Also I know that maybe the Taylor series expansion could help but differentiating that function leads to an awful mess.

$$z^2-\sqrt{2}\,z+2=(z-a)(z-b)\text{ where }a=\frac{\sqrt2+\sqrt6\,i}{2},\ b=\frac{\sqrt2-\sqrt6\,i}{2}.$$ Use partial fraction decomposition to write $$\frac{1}{z^2-\sqrt{2}\,z+2}=\frac{A}{z-a}+\frac{B}{z-b}.$$ Now expand in power series $1/(z-a)$ and $1/(z-b)$.