1. The problem statement, all variables and given/known data Find the residues of the function f(z), and compute the following contour integrals. a) the anticlockwise circle, centred at z = 0, of radius three, |z| = 3 b) the anticlockwise circle, centred at z = 0, of radius 1/2, |z| = 1/2 f(z) = 1/((z2 + 4)(z + 1)) ∫Cdz f(z) 2. Relevant equations ∫Cdz f(z) = 2πi ∑ Res(f, zi) (zi inside the contour C) 3. The attempt at a solution I have found the poles and hence the residues: z = 2i, -2i, -1 and the corresponding residues (respectively): -1/10 - i/20, -1/10 + i/20, 1/5 I'm fairly comfortable with these, however when computing the contour integrals using Cauchy's theorem I got that in a), all the poles lie in the contour and the sum of the residues = 0, so the contour integral = 0. But then with b), I found that because none of the poles lie in this circle of radius 1/2 (on the complex plane) then the contour integral also equals zero? I think I must have done something wrong as I wouldn't expected an assignment to have 2 zero answers! Thanks for any help.