Task 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:
Task 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.