If $z = x + iy$ and $|z - 2 + i| = |z - 3 - i|$,then the locus of $z$ is:

If $z$ and $\omega$ are two non-zero complex numbers such that $|z \omega|=1$ and $\operatorname{Arg}(z) - \operatorname{Arg}(\omega) = \frac{\pi}{2}$,then $\bar{z} \omega =$

If $|z - 3 - 4i| = 4$,where $i = \sqrt{-1}$,then the maximum possible value of $|z|$ is:

If $P(x, y)$ represents the complex number $z = x + i y$ in the Argand plane and $\operatorname{Arg} \left( \frac{z - 3 i}{z + 4} \right) = \frac{\pi}{2}$,then the equation of the locus of $P$ is

If the eight vertices of a regular octagon are given by the complex numbers $z_j = \frac{1}{x_j - 2i}$ for $j = 1, 2, \dots, 8$,where $x_j$ are the roots of $x^8 - 1 = 0$,then the radius of the circumcircle of the octagon is

Let $z \in \mathbb{C}$ be a complex number. The equation $2|z + 3i| - |z - i| = 0$ represents: