Product of Complex Conjugates

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

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

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

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

Then:

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