I'm having trouble with the following problem - I know how to show surjectivity, injectivity and thus bijectivity but I don't know how to apply it to this problem - help would be GREATLY appreciated!

Given U={z∈C : |z| = 1 }, n>0, f:U->U defined by f(z) = z^n and ~ the equivalence relation associated with f.

Show that f defines a bijection f-bar:U/~ -> U.

I don't know how to type mathematical notation so i hope you can understand it ok!