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Suppose-p-is-a-polynomial-with-complex-coefficients-and-an-even-degree-If-all-the-roots-of-p-are-complex-non-real-numbers-with-modulus-1-prove-that-p-1-R-iff-p-1-R-




Question Number 21309 by Tinkutara last updated on 20/Sep/17
Suppose p is a polynomial with complex  coefficients and an even degree. If all  the roots of p are complex non-real  numbers with modulus 1, prove that  p(1) ∈ R iff p(−1) ∈ R.
Supposepisapolynomialwithcomplexcoefficientsandanevendegree.Ifalltherootsofparecomplexnonrealnumberswithmodulus1,provethatp(1)Riffp(1)R.

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