Complex Modulus of Product of Complex Numbers

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

Let $$\left|{z}\right|$$ be the modulus of $$z$$.

Then $$\left|{z_1 z_2}\right| = \left|{z_1}\right| \cdot \left|{z_2}\right|$$.

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

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