# Complex Numbers prove $z^n+\bar z^n$ is a real number

My text book asks us to prove $z^n+\bar z^n$ is a real number where $\bar z$ is $z$ conjigate. $z$ is a nonzero complex number and $n$ is an integer

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Hint: $$z^n+\bar{z}^n=z^n+\overline{z^n}$$
Hint: Write $z=re^{i\theta}$.