Show that:

1. The additive group is isomorphic to the multiplicative group of all complex numbers of modulus 1.

2. The additive group is isomorphic to the multiplicative group of all complex roots of unity.

Okay, so I understand that I need find a mapping between these groups, prove they are well-defined, linear, and one to one and onto, but would anyone please explain to me how the complex numbers of mod 1 and roots of unity going to behave?

Complex numbers of mod 1, wouldn't that be any combination of a(i)?

Roots of unity, well, I know how it would work in integers, but complex, I'm a bit lost on that.

Thanks for all your help!!!