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 $\map \Re z$ be the real part of $z$.

Then:
 * $z + \overline z = 2 \, \map \Re z$

Proof
Let $z = x + i y$.

Then:

Also defined as
This result is also reported as:
 * $\map \Re z = \dfrac {z + \overline z} 2$