September 2023 A Let G be the set of the fifth roots of unity 1 Use de Moivre s formula to verify

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A Let G be the set of the fifth roots of unity 1 Use de Moivre s formula to verify 2023

A. Let G be the set of the fifth roots of unity. 1. Use de Moivre’s formula to verify that the fifth roots of unity form a group under complex multiplication, showing all work. 2. Prove that G is isomorphic to Z5 under addition by doing the following: a. State each step of the proof. b. Justify each of your steps of the proof. B. Let F be a field. Let S and T be subfields of F. 1. Use the definitions of a field and a subfield to prove that S ∩ T is a field, showing all work

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