Complex Conjugation is Involution

Theorem
Let $z = x + iy$ be a complex number.

Let $\overline z$ denotes the complex conjugate of $z$.

Let $\overline {\cdot} :\C \to \C : z \mapsto \overline z$ be the complex conjugation.

Then $\overline{\cdot}$ is an involution, i.e.:


 * $\overline{\overline z} = z$