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Ryan, Engineer

Category: Calculus and Above

Satisfied Customers: 9046

Experience: B.S. in Civil Engineering

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I am trying to prove isomorphism between a fifth root of

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I am trying to prove isomorphism between a fifth root of unity and z sub 5 under addition. I know I have to show one to one, onto, and homomorphism. But I can't seem to get started. I've already proven that the fifth root of unity is a group, using de moivre's formula, but I can't seem to wrap my head around how to map between the two groups to find my one-to-one.

Unfortunately, I will need to see more. I kind of know that equation already, since it's the derivation of de Moivre's formula for the fifth roots of unity. But the actual problem I'm having is how to use it to map from the group to the Z5 under addition. So I guess I need to see how you plug one in to get the other?