complex numbers

In polar coordinates:  $z=re^{i\theta} \text{ and } \bar{z} = re^{-i\theta}$   so $(\bar{z})^n=(re^{-i\theta})^n=r^ne^{-in\theta}$ and $\bar{z^n}=\bar{(r^ne^{in\theta})}=r^ne^{-in\theta}$