A+ Answers

 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.