Fields are an important algebraic structure, and complex numbers have that structure.
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 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.
This material may consist of step-by-step explanations on how to solve a problem or examples of proper writing, including the use of citations, references, bibliographies, and formatting. This material is made available for the sole purpose of studying and learning - misuse is strictly forbidden.Let S and T be subfields of F.
We first show that the intersection of S and T is non-empty. Let 0 denote the identity element with respect to addition in F. Since S and T are both subfields of F, each must contain 0, and therefore 0 is in the intersection.
We next show that the intersection is a commutative ring.
First the intersection is closed under addition + and multiplication...