Complex Analysis Answers

"\\intop" 1/(3-2cos"\\theta" +sin"\\theta" ) using contour integration limit 0 to 2pi

expand f(z)=z/(z-1)(2-z) in a laurent series valid 1<|z|<2

find the residue of f(z) =1/(z²+1)² at z=i

Find the laurent series about the indicated singularity for the function e^2z/(z-1)³ at z=1

Evaluate the integral "\\oint" 1/(z²+1)(z²-4)dz where |z|=1.5

determine the poles and the residues at each pole of the function f(z)=z²-2z/(z+1)²(z²+4)

1/z(e^z-1) at its poles

by contour techniques "\\int" 1/(2+cos"\\theta" ) limit 0 to 2"\\pi"

Evaluate the integral "\\oint" e^zt/z²+1 dz where c is the circle |z|=3.

Show that f(z)=z²(e^z-1) is differentiable at z_o=0. Check whether f is analytic at O.