- #1

mindauggas

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## Homework Statement

If [itex]P(x)[/itex] is a polynomial with real coefficients, then if [itex]z[/itex] is a complex zero of [itex]P(x)[/itex], then the complex conjugate [itex]\bar{z}[/itex] is also a zero of [itex]P(x)[/itex].

## Homework Equations

Book provides a hint: assume that [itex]z[/itex] is a zero for [itex]P(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+...+a_{1}x+a_{0}[/itex] and use the fact that [itex]\bar{z}=z[/itex] if [itex]z[/itex] is real (since every real can be written as a complex number with a zero imaginary part) and that [itex]\overline{z+w}=\bar{z}+\bar{w}[/itex] and [itex]\overline{z*w}=\bar{z}*\bar{w}[/itex] for all complex numbers.

## The Attempt at a Solution

Well, it is proven for any real since the complex conjugate of a real number is that same number.

I'm lost from here.