Let's up the difficulty for this one, shall we?

$\displaystyle \int _{|z|=1} \frac{6z^{98}}{23z^{99} -2z^{81} + z^4 - 7}~dz$

(where z is a complex variable)

(Source: Mathematics Stack Exchange )

Hint: What does Rouche's theorem say about the zeros of the denominator?

-Dan