The argument of the complex number $ - 1 + i\sqrt 3 $ is ............. $^\circ$

If ${z_1},{z_2}$ and ${z_3},{z_4}$ are two pairs of conjugate complex numbers, then $arg\left( {\frac{{{z_1}}}{{{z_4}}}} \right) + arg\left( {\frac{{{z_2}}}{{{z_3}}}} \right)$ equals

If $|z|\, = 4$ and $arg\,\,z = \frac{{5\pi }}{6},$then $z =$

If a complex number $z$ statisfies the equation $x + \sqrt 2 \,\,\left| {z + 1} \right|\,+ \,i\, = \,0,$ then $\left| z \right|$ is equal to

The modulus and amplitude of $\frac{{1 + 2i}}{{1 - {{(1 - i)}^2}}}$ are

If $(3 + i)z = (3 - i)\bar z,$then complex number $z$ is