Let F be a field. Let S and Tbe subfields of F. Use the definitions of a field and a subfield

A. Use de Moivre’s formula to verify that the 5th roots of unity form a group under complex multiplication, showing all work.

B. Let F be a field. Let S and Tbe subfields of F. Use the definitions of a field and a subfield to prove that S ? T is a field, showing all work.