I'm confused as to how to go about answering #2 and #3, and I'm not confident in my approach to #1.
Help!
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 Let F be a field. Let S and T be subfields of F.
3. Use the definitions of a field and a subfield to prove that S ∩ T is a field, showing all work.