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

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

If $Z = \frac{-2}{1 + \sqrt{3}i}$,where $i = \sqrt{-1}$,then the value of $\arg(Z)$ is

If $z_1, z_2$ and $z_3, z_4$ are $2$ pairs of complex conjugate numbers,then $\arg \left( \frac{z_1}{z_4} \right) + \arg \left( \frac{z_2}{z_3} \right)$ equals

Find the modulus and argument of the complex number: $\frac{1+i}{1-i}$

Let the two values of $z = \sqrt{\frac{1-i}{1+i}}$ be $z_1$ and $z_2$. If $-\frac{\pi}{2} < \operatorname{Arg}(z_1) < \operatorname{Arg}(z_2) < \pi$,then $\arg(z_1) + \arg(z_2) = $