Let $U_{1}$ be the circle group on $\mathbb{C}^\times$
For my mathimatics study, I have to prove that there is an isomorphism
f: $U_{1}\times \mathbb{R}^+$ $\rightarrow$ $\mathbb{C}^\times$
How do I prove this?
I was thinking of f(θ, r) = re^(2πiθ), since all elements on C are of the form re^θi, but maybe there is a much easier proof.
Thanks in advance!