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Question Number 21309 by Tinkutara last updated on 20/Sep/17

$$\mathrm{Suppose}p\mathrm{is}\mathrm{a}\mathrm{polynomial}\mathrm{with}\mathrm{complex}$$$$\mathrm{coefficients}\mathrm{and}\mathrm{an}\mathrm{even}\mathrm{degree}.\mathrm{If}\mathrm{all}$$$$\mathrm{the}\mathrm{roots}\mathrm{of}p\mathrm{are}\mathrm{complex}\mathrm{non}-\mathrm{real}$$$$\mathrm{numbers}\mathrm{with}\mathrm{modulus}1,\mathrm{prove}\mathrm{that}$$$$p\left(1\right)\in R\mathrm{iff}p(-1)\in R.$$

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