Complex Analysis Answers

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.

Find zeros of f(z)=sin hz

Evaluate the integral 1/2"\\pi" i"\\oint"dz /z²(z²+2z+3), where c is the circle |z|=3.

By contour techniques"\\smallint" 1/(2+cos"\\theta") limit 0 to 2"\\pi" .

Evaluate the "\\oint"(12z-7)/(z-1)2(2z+3) dz where c is the circle |z+i|= Sqrt3

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