# Complex Calculus - using Rouche theorem

The question is:

by using rouche 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 theoremm 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 $\Im(z)> 0$.

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