1. The problem statement, all variables and given/known data Let G be the group of real numbers under addition and let N be the subgroup of G consisting of all the integers. Prove that G/N is isomorphic to the group of all complex numbers of absolute value 1 under multiplication. Hint: consider the mapping f: R-->C given by f(x)=e^[2pi(ix)] 3. The attempt at a solution So this says that a subgroup of Z is normal in R. G/N is the quotient group of left cosets of N in G. And I want to prove that G/N is isomorphic to (a+bi)(c+di) <---not sure if this is what I want to prove...but if it is then...it equals ac+adi+bci-bd= +/- 1 Which implies ac+adi+bci-bd=ac-bd=+/- 1 Am I thinking of this right so far? I'm not sure how to use the hint.