Mathematics - Complex Analysis - Cauchy's theorem and residues - Residue Computations

8 problems: (1) 'Find singularities of f(z)=1/(z²-1).' (Poles at z=±1). (2) 'Find residue of 1/(z-2) at z=2.' (3) 'Find residue of z/(z²+4) at z=2i.' (4) 'Evaluate ∮ 1/(z-1) dz around |z|=2 using residue theorem.' (2πi). (5) 'Evaluate ∮ 1/(z-1) dz around |z|=0.5.' (0, pole not inside). (6) 'Find res