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:

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

Convert the given complex number in polar form: $-1+i$

If $z_1 = 5 - 2i$ and $z_2 = 3 + i$,where $i = \sqrt{-1}$,then $\arg \left(\frac{z_1 + z_2}{z_1 - z_2}\right)$ is

Assertion $(A)$: If the arguments of $\bar{z}_1$ and $z_2$ are $\frac{\pi}{5}$ and $\frac{\pi}{3}$ respectively,then $\arg(z_1 z_2)$ is $\frac{2\pi}{15}$. Reason $(R)$: For any complex number $z$,$\arg(\bar{z}) = \frac{\pi}{2} + \arg(z)$. The correct option among the following is:

The locus of the variable point $z=x+iy$ whose amplitude is always equal to $\theta$,is