# Proof of orientation-reversing isometries and their general form

Show that each orientation-reversing isometry has the form

$\bar f(z)=c+e^{i\theta}\bar z$, which becomes

$\bar g(z)=ce^{-i(\theta/2)}+\bar z$ after rotation of axes and

$\bar h(z)==\alpha+\bar z$, where $\alpha \in \mathbb R$, after translation of O.

I don't understand even where to start, I don't understand orientation-reversaing isometries, and I don't understand the significance of "$==$"