Let $z = x + iy$,where $x$ and $y$ are real. The points $(x, y)$ in the $X-Y$ plane for which $\frac{z+i}{z-i}$ is purely imaginary,lie on

If $z_1=2-3i$ and $z_2=-1+i$,then the locus of a point $P$ represented by $z=x+iy$ in the Argand plane satisfying the equation $\arg \left(\frac{z-z_1}{z-z_2}\right)=\frac{\pi}{2}$ is

The locus of the point $z=x+iy$ satisfying the equation $\left|\frac{z-1}{z+1}\right|=1$ is given by :

The locus of the complex number $Z$ such that $\arg \left(\frac{Z-1}{Z+1}\right)=\frac{\pi}{4}$ is

If the locus of $z \in \mathbb{C}$, such that $\operatorname{Re}\left(\frac{z-1}{2 z+i}\right)+\operatorname{Re}\left(\frac{\bar{z}-1}{2 \bar{z}-i}\right)=2$, is a circle of radius $r$ and center $(a, b)$, then $\frac{15 a b}{r^2}$ is equal to :

Let $z=x+iy$ and a point $P$ represent $z$ in the Argand plane. If the real part of $\frac{z-1}{z+i}$ is $1$,then a point that lies on the locus of $P$ is