Use de Moivres formula to verify that the fifth roots of unity form a group under complex multiplication, showing all work.

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Use de Moivres formula to verify that the fifth roots of unity form a group under complex multiplication, showing all work.

A. Let G be the set of the fifth roots of unity.1. Use de Moivres 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 Z under addition by doing the following:a. State step of the proof.b. Justify of your steps of the proof.B. Let be a field. Let and be subfields of .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.