Quotient group of the non-zero complex numbers

Question

Let $\mathbb{C}$ denote the multiplicative group of non-zero complex numbers and let $P$ denote the subgroup of positive (real) numbers. I am trying to find the quotient group $\mathbb{C}/P$. Please help.

Answer 1

Hint: Every complex number has the form $re^{i\theta}$. You can dispense with that $r$...