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

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

Proof
Let $$z = x + i y$$.

Then:

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