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QUESTION

Let G be the set of the fifth roots of unity. Use de Moivre's formula to verify that the fifth roots of unity form a group under complex...

Task:

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.

C.  When you use sources, include all in-text citations and references in APA format.

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