Hee I have not yet a good idea how to start on this one.
Let a rational function with .
Show that the sum of the residues of f is zero.
Some guiding hints will be very much appreciated.
Integrate f round a circle centred at the origin, with really large radius R. On the circle, , so the absolute value of the integral will be of order 1/R. As R goes to infinity, the contour contains all the singularities, and the integral ( (sum of residues)) goes to 0.