If $z = x + iy$ and $|z - zi| = 1,$ then

If $Z \neq \pm 1$ is a complex number and $\operatorname{Arg}\left(\frac{Z-1}{Z+1}\right)=\frac{\pi}{4}$,then the locus of $Z$ in the Argand plane is

If a complex number $z$ is such that $\frac{z-2i}{z-2}$ is a purely imaginary number and the locus of $z$ is a closed curve,then the area of the region bounded by that closed curve and lying in the first quadrant is

If $z=x+iy$ and if the point $P$ in the Argand plane represents $z$,then the locus of $P$ satisfying the equation $|z-3i|+|z+3i|=10$ is

Let $S = \{z = x + iy : \frac{2z - 3i}{4z + 2i} \text{ is a real number} \}$. Then which of the following is $NOT$ correct?

Let $z \in \mathbb{C}$ be such that $|z| < 1$. If $w = \frac{5 + 3z}{5(1 - z)}$,then