If $\alpha $ and $\beta $ are different complex numbers with $|\beta | = 1$, then $\left| {\frac{{\beta - \alpha }}{{1 - \overline \alpha \beta }}} \right|$ is equal to
$0$
$3$
$1$
$2$
If ${(\sqrt 8 + i)^{50}} = {3^{49}}(a + ib)$ then ${a^2} + {b^2}$ is
If $z$ is a complex number such that ${z^2} = {(\bar z)^2},$ then
If $z_1, z_2, z_3$ $\in$ $C$ such that $|z_1| = |z_2| = |z_3| = 2$, then greatest value of expression $|z_1 - z_2|.|z_2 - z_3| + |z_3 - z_1|.|z_1 - z_2| + |z_2 - z_3||z_3 - z_1|$ is
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
Find the conjugate of $\frac{(3-2 i)(2+3 i)}{(1+2 i)(2-i)}$.