Homework

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