Complex Analysis Answers

Determine the poles and the residue at each pole of the function f(z)=1/(z-1)²(z+2)

Find the residue of the function f(z)=1/z(e^z-1)

Prove ∇^2{FG} = F ∇^2 F + 2∇F•∇G

Find a function v such that f(z) = u+iv is analytic [i.e. find the conjugate function of u ].

find the residue of the function f(z)=1/z(z-2) where c is the circle |z|=1

prove that the function u = 2x (1-y) is harmonic

Say true or false, with a short proof.

All the cube roots of I in C are z₁ = cos(π/2)+ i sin(π/2) , z₂ = cos (π/6)+ isin(π/6) and z₃ = cos (5π/6)+i sin (5π/6)

Find all the cube roots of

find the value for z and w for 4z-1 = -2iw

If f(z)= 1/\sqrt{|z-1} find the domain of definition of f.