If $z$ is a complex number, then $(\overline {{z^{ - 1}}} )(\overline z ) = $

If $|z_1|=1, \, |z_2| =2, \,|z_3|=3$ and $|9z_1z_2 + 4z_1z_3+z_2z_3| =12$ then the value of $|z_1+z_2+z_3|$ is equal to :-

If $\frac{{z - \alpha }}{{z + \alpha }}\left( {\alpha  \in R} \right)$ is a purely imaginary number and $\left| z \right| = 2$, then a value of $\alpha $ is

Let $z$ be a complex number with non-zero imaginary part. If $\frac{2+3 z+4 z^2}{2-3 z+4 z^2}$ is a real number, then the value of $|z|^2$ is. . . . . 

Let ${z_1}$ and ${z_2}$ be two complex numbers with $\alpha $ and $\beta $ as their principal arguments such that $\alpha + \beta > \pi ,$ then principal $arg\,({z_1}\,{z_2})$ is given by

The conjugate of a complex number is $\frac{1}{{i - 1}}$ then that complex number is