The question is:
By using Rouché's theorem, calculate number of zeros $F(z)=(z^2 + 2)(z^2 > + 1) - iz(z^2 + 2)$
where $D={\Im(z)> 0}$.
How do I need to choose $h(z)$ and $g(z)$ s.t $F= h + g$ so I can apply the theorem and what about the condition $D={\Im(z)> 0}$?
I know the application of rouche theorem when we have condition on $|z|$, for example $1<|z|<2$ but I don't know what I need to do with the condition $\Im(z)> 0$.