If $arg(z) < 0$,then $arg(-z) - arg(z)$ equals

If $-\pi < \arg (z) < -\frac{\pi}{2}$,then $\arg (\bar{z}) - \arg (-\bar{z})$ is

If $z=x+iy$,where $x, y \in \mathbb{R}$ and the point $P$ in the Argand plane represents $z$,then the locus of $P$ satisfying the condition $\arg \left(\frac{z-1}{z-3i}\right)=\frac{\pi}{2}$ is:

If $0 < \text{amp}(z) < \pi$,then $\text{amp}(z) - \text{amp}(-z) = $

Let $z$ and $w$ be two complex numbers such that $\bar{z}+i \bar{w}=0$ and $\operatorname{Arg}(z w)=\pi$. Then,$\operatorname{Arg} z=$

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