Residues and the residue theorem
General · Mathematics
Study notes
Q: Compute ∮_C(z/(z²+1))dz, C: |z| = 2 (counterclockwise). Poles: z = ±i, both inside |z|=2! Res at i: lim(z-i)z/((z-i)(z+i)) = i/(2i) = 1/2. Res at -i: -i/(-2i) = 1/2. ∮ = 2πi(1/2+1/2) = 2πi! (Residue theorem: sum residues × 2πi!)