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

$|{z_1} + {z_2}| = |{z_1}| + |{z_2}|$ is possible if

If the points $P_1$ and $P_2$ represent two complex numbers $z_1$ and $z_2$ respectively,then the point $P_3$ represents the number

The locus of the complex number $z$ such that $\arg \left(\frac{z-2}{z+2}\right)=\frac{\pi}{3}$ is:

If the point $P$ denotes the complex number $z=x+iy$ in the Argand plane and $\frac{z-(2-i)}{z+(1+2i)}$ is a purely imaginary number,then the locus of $P$ is

The complex number $z = x + iy$ which satisfies the equation $\left| \frac{z - 5i}{z + 5i} \right| = 1$ lies on