Sum of Complex Conjugates

Theorem
Let $$z_1, z_2 \in \C$$ be complex numbers.

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

Then $$\overline {z_1 + z_2} = \overline {z_1} + \overline {z_2}$$.

Proof
Let $$z_1 = x_1 + i y_1, z_2 = x_2 + i y_2$$.

Then:

$$ $$ $$ $$