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

$z=x+iy$ and the point $P$ represents $z$ in the Argand plane. If the amplitude of $\left(\frac{2z-i}{z+2i}\right)$ is $\frac{\pi}{4}$,then the equation of the locus of $P$ is

If ${Z_1} \ne 0$ and ${Z_2}$ are two complex numbers such that $\frac{{{Z_2}}}{{{Z_1}}}$ is a purely imaginary number,then $\left| {\frac{{2{Z_1} + 3{Z_2}}}{{2{Z_1} - 3{Z_2}}}} \right|$ is equal to

The locus of the point representing the complex number $z$ for which $|z+3|^2-|z-3|^2=15$ is

If the complex numbers $z_1, z_2, 0$ are vertices of an equilateral triangle,then $z_1^2 + z_2^2 =$

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