Given $z$ is a complex number such that  $|z| < 2,$ then the maximum value of $|iz + 6 -8i|$ is equal to-

If $|{z_1}|\, = \,|{z_2}|$ and $arg\,\,\left( {\frac{{{z_1}}}{{{z_2}}}} \right) = \pi $, then ${z_1} + {z_2}$ is equal to

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

If $\frac{{z - i}}{{z + i}}(z \ne - i)$ is a purely imaginary number, then $z.\bar z$ is equal to

Let $z$ be a purely imaginary number such that ${\mathop{\rm Im}\nolimits} (z) < 0$. Then $arg\,(z)$ is equal to

Let $z$ be a complex number such that $\left| z \right| + z = 3 + i$ (where $i = \sqrt { - 1} $). Then $\left| z \right|$ is equal to