complex variables siverman book please help me tutors thank

complex variables siverman book
please help me !! tutors!! thanks
show all steps please

G. Discuss the imageot the circle tor the foliomnas 6. Discuss the image of the circle ll for the following multiple-valued functions (a) wz,n a positive integer a) w \"m a positive integer (b) w (b) w-z

Solution

(1) w=z^1/n

So |w| = |z|^1/n = r^1/n

So w maps the given circle onto (because we can always take the nth root of unity) the circle , centre 0 and radius r^1/n

(ii) Same considerations apply and the image is the circle |w| = r^2/3