Is $|z\bar{z}^{-1}|=1,z\in\mathbb{C}$?

Question

$\bar{z}$ is the conjugation of $z$.

Thank you so much

Answer 1

HINT

Use that with $\bar z \ne 0$

$$|z\bar{z}^{-1}|=|z||\bar{z}^{-1}|=\frac{|z|}{|\bar{z}|}$$

Answer 2

Note that $|z|=|\bar{z}| \space \forall z \in \mathbb{C}$ and $\left| \frac{z_1}{z_2} \right| = \frac{|z_1|}{|z_2|} \space \forall z_1, z_2 \in \mathbb{C}, z_2 \ne 0$