# easy partial fraction decomposition of complex fraction

I should make a partial fraction decomposition of the following fraction where $z\in \mathbb{C}$. I am not able to start or do something because I am not able to factorize $z²+4$. Does anybody has any suggestions??

$$\frac{1}{z^{2}+4}$$

Notice that $z^2+4=(z+2i)(z-2i)$. You can use the normal formula for the roots of a quadratic equation and use that $\sqrt{-1}=i$.