Difference of Complex Number with Conjugate

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

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

Let $\operatorname{Im} \left({z}\right)$ be the imaginary part of $z$.

Then
 * $z - \overline z = 2 i \operatorname{Im} \left({z}\right)$

Proof
Let $z = x + i y$.

Then:

Also defined as
This result is also reported as:
 * $\operatorname{Im} \left({z}\right) = \dfrac {z - \overline z} {2 i}$