(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Homework Help: Isomorphism of quotient group

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