Complex Analysis Answers

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.

Find the closure of the following set in C

{0, 1/1 , 1/2 , 1/3 ,.........}

Find the closure of the following set in C

{z∈C : (ReZ)²=ImZ}