The equation $\overline{b}z + b\overline{z} = c$,where $b$ is a non-zero complex constant and $c$ is real,represents:

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

If $\operatorname{Re}\left(\frac{z-1}{2z+i}\right)=1,$ where $z=x+iy,$ then the point $(x, y)$ lies on a

The points $z_1, z_2, z_3, z_4$ in the complex plane are the vertices of a parallelogram taken in order,if and only if

If ${z_1}$ and ${z_2}$ are two complex numbers such that $\left| \frac{{z_1} - {z_2}}{{z_1} + {z_2}} \right| = 1$ and $i{z_1} = k{z_2}$,where $k \in R$,then the angle between ${z_1} - {z_2}$ and ${z_1} + {z_2}$ is

The equation of the locus of $z$ such that $\left|\frac{z-i}{z+i}\right|=2$,where $z=x+iy$ is a complex number,is