Determine the power series expansion of $\displaystyle f(z)$ at $\displaystyle z_0$ without computing derivatives

(i) $\displaystyle f(z) = sinz ,$ $\displaystyle z_0 = i;$

(ii)$\displaystyle f(z )= \frac{1}{z^2-3z+2} ,$ $\displaystyle z_0 = 0;$

(iii)$\displaystyle f(z) = Log z, $ $\displaystyle z_0 = 1;$

So how the heck would I do this? If someone could show me step by step how to do one of them I'm pretty sure I could do the rest, but I don't know how to do it without derivatives as I would have just taken the taylor series