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Homework Statement
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)]
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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