complex analysis - Imaginary Part of log(f(z))

Let

$f(z)=z^2+4$

My question is, how the picture of

$M=\{z\in\mathbb C:\operatorname{Im}(\log(f(z)) > 0\}$ looks like.

My attempt is that
$\operatorname{Im}(\log(f(z))=\arg(f(z))$
which let's me guess, that $\operatorname{Im}(f(z))$ and $\operatorname{Re}(f(z))$ both had to be greater than zero or smaller than zero, as $\arctan(x) > 0$, if $x>0$.
Can anyone help me with this issue?
Thanks a lot.