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Let $C$ be the ellipse $9x^2+4y^2=36$ traversed once in the counterclockwise direction. Define the function $g$ by $$g(z)=\int_{C}\frac{s^2+s+1}{s-z}ds.$$

Find $g(4i)$.

Well I know I must find $g(z)$ (that is the integral) before computing $g(4i)$, so I decided to use Cauchy's integral formula $f(z_{0})=\frac{1}{2\pi i}\int_C\frac{f(z)}{z-z_{0}}dz$. This put me into trouble, because I do not how to start. Please i need a hint.

Thanks.

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    Try putting in the $4i$ first, then evaluating the integral. It's a lot easier this way because then you're working with a specific integral.2012-03-24
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    @Hassan To make it more familiar, start with changing $z$ with $z_0$ and $s$ with $z$.2012-03-24
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    @PeterT.off: I will try it.2012-03-24
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    Also you should remember if f(z)/(z-z_0) is analytic within and on C, then the integral is 0.2012-03-24

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