MATH 001 Fields are an important algebraic structure
Fields are an important algebraic structure, and complex numbers have that structure.
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.