Product of Complex Conjugates/Examples/3 Arguments/Proof 2

Theorem

Let $z_1, z_2, z_3 \in \C$ be complex numbers.

Let $\overline z$ denote the complex conjugate of the complex number $z$.

Then:

$\overline {z_1 z_2 z_3} = \overline {z_1} \cdot \overline {z_2} \cdot \overline {z_3}$

Proof

From Product of Complex Conjugates: General Result:

$\ds \overline {\prod_{j \mathop = 1}^n z_j} = \prod_{j \mathop = 1}^n \overline {z_j}$

The result follows by setting $n = 3$.