Sorry I don't have equation editor, for some reason every time I install it on Microsoft Word it never appears... 1. The problem statement, all variables and given/known data Calculate the residue at each isolated singularity in the complex plane e^(1/z) 2. Relevant equations #1 Simple pole at z0 then, Res[f(z), z0] = lim (z - z0)(f(z)) as z goes to z0. #2 Double pole at z0 then, Res[f(z), z0] = lim d/dz [(z - z0)^2*f(z)] as z goes to z0. #3 If f(z) and g(z) are analytic at z0, and if g(z) has a simple zero at z0 then Res[f(z)/g(z), z0] = f(z0)/g'(z0) #4 If g(z) is analytic and has a simple zero at z0, then Res[1/g(z), z0] = 1/g'(z0). 3. The attempt at a solution The problem occurs when z = 0 so looking at Res[e^(1/z), 0], Using #1, #3, #4 don't help the problem. So using #2 lim as z goes to z0 [d/dz z^2 * e^(1/z)], there's still a problem... I'm completely lost at this point. 1. The problem statement, all variables and given/known data Evaluate the following integral, using the residue theorem Integral |z| = 1 (sin(z)/z^2)dz 2. Relevant equations See Above 3. The attempt at a solution How would I start this? z = 0 gives a problem, would I take the integral first and then evaluate?