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 $\alpha$ and $\beta$ are different complex numbers with $|\beta|=1,$ then find $\left|\frac{\beta-\alpha}{1-\bar{\alpha} \beta}\right|$

The argument of the complex number $\frac{{13 - 5i}}{{4 - 9i}}$is

The amplitude of $\frac{{1 + \sqrt 3 i}}{{\sqrt 3 + 1}}$ is

If $z=\frac{1}{2}-2 i$, is such that $|z+1|=\alpha z+\beta(1+i), i=\sqrt{-1}$ and $\alpha, \beta \in R \quad$, then $\alpha+\beta$ 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