For any complex number $z,\bar z = \left( {\frac{1}{z}} \right)$if and only if

Let ${z_1}$ be a complex number with $|{z_1}| = 1$ and ${z_2}$be any complex number, then $\left| {\frac{{{z_1} - {z_2}}}{{1 - {z_1}{{\bar z}_2}}}} \right| = $

If $z$ and $\omega $ are two non-zero complex numbers such that $|z\omega |\, = 1$ and $arg(z) - arg(\omega ) = \frac{\pi }{2},$ then $\bar z\omega $ is equal to

If $\frac{{2{z_1}}}{{3{z_2}}}$ is a purely imaginary number, then $\left| {\frac{{{z_1} - {z_2}}}{{{z_1} + {z_2}}}} \right|$ =

If the set $\left\{\operatorname{Re}\left(\frac{z-\bar{z}+z \bar{z}}{2-3 z+5 \bar{z}}\right): z \in C , \operatorname{Re}(z)=3\right\}$ is equal to the interval $(\alpha, \beta]$, then $24(\beta-\alpha)$ is equal to

The inequality $|z - 4|\, < \,|\,z - 2|$represents the region given by