Consider any complex number \[ z, \ \]with modulus

\[ \sqrt{z\bar{z} } = |z| = r \ ,\]

where \[ r \in \mathbb{R^{+}}\ . \]

Note that \[ \frac{z}{r} \ \]would be a complex number with modulus one:

\[ | \frac{z}{r} | = | \frac{z}{|z|} | = 1. \]

Consider any complex number \[ z, \ \]with modulus

\[ \sqrt{z\bar{z} } = |z| = r \ ,\]

where \[ r \in \mathbb{R^{+}}\ . \]

Note that \[ \frac{z}{r} \ \]would be a complex number with modulus one:

\[ | \frac{z}{r} | = | \frac{z}{|z|} | = 1. \]