Roots of unity are complex numbers that when raised to some positive integer power are equal to one. Cyclotomic polynomials are irreducible polynomials with integer coefficients constructed using primitive roots of unity, a more specific type of root of unity. Their interesting properties and use in the factorization of another set of polynomials have led to fascinating and impactful mathematical study. Through adjoining a primitive root of unity to the set of rational numbers, one can create a new cyclotomic field.
