A problem I'm working on requires me to evaluate the following complex integral about some closed contour:
$$\oint f(z)dz$$ where $$f(z) = \left(V-\frac{Va^2}{z^2}\right)^2$$ and $V$ and $a$ are real constants.
No particular drawing or suggestion as to the choice of contour was provided so right now I'm stuck as to how to even begin evaluating the integral. Any help would be much appreciated.
If the contour contains $0$ the the integral does not exist. If it does not contain $0$ then the integral is $0$. This is because when you expand the square you see that each term is the derivative of some function. The integral of a derivative over any closed contour is $0$.