Modulus of a product

Computation.
$$|zw|^2=(zw)\overline{(zw)}=zw\bar z\bar w=(z\bar z)(w\bar w)=|z|^2|w|^2.$$
Since moduli are nonnegative, $|zw|=|z||w|$.

Conclusion. The modulus is multiplicative: $|zw|=|z||w|$. Consequently $|z/w|=|z|/|w|$ for $w\neq0$, and $|z^n|=|z|^n$.