Thank you!!!
What if it were a bit more complicated?
For example,
$\displaystyle \frac{(z-3i)^2}{(z^2+4)^2}$?
I do not really know.
I know you can always use the definition, i.e. $\displaystyle f'(z)= \lim _{h \to 0} \frac{f(z+h)-f(z)}{h}$ where $\displaystyle f(z)=\frac{(z-3i)^2}{(z^2+4)^2}$. Of course $\displaystyle h\in \mathbb{C}$.