If $z$ is a complex number such that $| z | = 4$ and $arg \,(z) = \frac {5\pi }{6}$ , then $z$ is equal to

Let $z$ be complex number such that $\left|\frac{z-i}{z+2 i}\right|=1$ and $|z|=\frac{5}{2} \cdot$ Then the value of $|z+3 i|$ is 

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

If ${z_1},{z_2},{z_3}$ are complex numbers such that $|{z_1}|\, = \,|{z_2}|\, = $ $\,|{z_3}|\, = $ $\left| {\frac{1}{{{z_1}}} + \frac{1}{{{z_2}}} + \frac{1}{{{z_3}}}} \right| = 1\,,$ then${\rm{ }}|{z_1} + {z_2} + {z_3}|$ is

If$z = \frac{{1 - i\sqrt 3 }}{{1 + i\sqrt 3 }},$then $arg(z) = $ ............. $^\circ$

Argument and modulus of $\frac{{1 + i}}{{1 - i}}$ are respectively