If $z$ is a purely real number such that $\text{Re}(z) < 0$,then $\text{arg}(z)$ is equal to

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

If $z = \sqrt{2} \sqrt{1 + \sqrt{3} i}$ represents a point $P$ in the Argand plane and $P$ lies in the third quadrant,then the polar form of $z$ is

The amplitude of $\sin \frac{\pi}{5} + i(1 - \cos \frac{\pi}{5})$ is

Let $z_0$ be a root of the quadratic equation,$x^2 + x + 1 = 0$. If $z = 3 + 6iz_0^{81} - 3iz_0^{93}$,then $\arg(z)$ is equal to

Let $z = 1 + i$ and $z_1 = \frac{1 + i \overline{z}}{\overline{z}(1 - z) + \frac{1}{z}}$. Then $\frac{12}{\pi} \arg(z_1)$ is equal to $..........$.