Find the domain of analyticity of the function Are the integ

Find the domain of analyticity of the function. Are the integrals of this function path independent in the domain? Are they path independent in the disk |z|

Solution

1. The function f(z) is not continuous at z=1 and z=3, so the domain of analyticity is C-{1, 3}.

The integrals of this function within the domain are path independent, since f(z) is continous in the domain.

They are not independent in the disk |z|<2, since it contain the point z=1 at which f(z) is not continuous.