Reference no: EM13801907
Fields are an important algebraic structure, and complex numbers have that structure.
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.
A review of complex numbers in polar form may be necessary. If you already understand "angles add when you multiply in polar form" then you're okay.
Make sure you also understand deMoivre's Formula so you know how to do exponents. Roots are the opposite of exponents, so to understand roots, you need to understand, and reverse-engineer, deMoivre's Formula.
You need to confirm that the 5th roots of unity form a group under the operation of complex multiplication.
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