Sum of Complex Number with Conjugate

Theorem
Let $z \in \C$ be a complex number.

Let $\overline {z}$ be the complex conjugate of $z$.

Let $\Re \left({z}\right)$ be the real part of $z$.

Then:
 * $z + \overline z = 2 \Re \left({z}\right)$

Proof
Let $z = x + i y$.

Then: