Let $z$ be a purely imaginary number such that $\text{Im}(z) > 0$. Then $\text{arg}(z)$ is equal to

If $z=1+i \sqrt{3}$ then $|\operatorname{Arg} z|+|\operatorname{Arg} \bar{z}|$ is equal to

Let $z_1$ and $z_2$ be two complex numbers with $\alpha$ and $\beta$ as their principal arguments such that $\alpha + \beta > \pi$,then the principal argument of $z_1 z_2$ is given by:

The amplitude of the complex number $z = \sin \alpha + i(1 - \cos \alpha )$ is

The amplitude (argument) of $(1+i)^{5}$ is

Let $z$ be a complex number such that the principal value of argument, $\arg(z) > 0$. Then, $\arg(z) - \arg(-z)$ is