If z is a non-zero complex number, then

(a) $\left|\frac{\bar{z}}{z}\right|$

$\left|\frac{|\bar{z}|^{2}}{z \bar{z}}\right|=\left|\frac{|\bar{z}|^{2}}{|z|^{2}}\right| \quad\left(\because z \bar{z}=|z|^{2}\right)$

Let $z=a+i b$

$\Rightarrow|z|=\sqrt{a^{2}+b^{2}}$

Let $\bar{z}=a-i b$

$\Rightarrow|\bar{z}|=\sqrt{a^{2}+b^{2}}$

$\therefore\left|\frac{|\bar{z}|^{2}}{z \bar{z}}\right|=\left|\frac{|\bar{z}|^{2}}{|z|^{2}}\right|$

$=\left|\frac{\bar{z}}{z}\right|$