A. Let G be the set of the fifth roots of unity. 1. Use de Moivres 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
