Write the Laurent series expansion for the following functions $\displaystyle f(z)$ centered at $\displaystyle z_0$. State what are the possible domains.

(a) $\displaystyle f(z) = \frac{z}{5z+1}$ $\displaystyle z_0=1$

(b) $\displaystyle g(z) = \frac{z}{z^2-3iz-2}$ $\displaystyle z_0=0$

I know how to do part (a) when $\displaystyle z_0=0$ but I do not see how to do it when $\displaystyle z_0=1$. For part (b), I used the quadratic formula, then I did not know how to finish the problem. I need a push in the right direction. Thanks in advance.