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Reciprocal PolynomialIn mathematics, for a polynomial p with complex coefficients, -
we define -
where denotes the complex conjugate of A polynomial is called reciprocal if p(z) = p*(z). If the coefficients ai are real then this reduces to ai = an-i. If p(z) is the minimal polynomial of z0 with |z0| = 1, and p(z) has real coefficients, then p(z) is reciprocal. This follows because, - .
So z0 is a root of the polynomial which has degree n. But, the minimal polynomial is unique, hence -
A consequence is that the cyclotomic polynomials are reciprocal for .
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