If $z=x+iy$,then the equation $|z+1|=|z-1|$ represents

If $\omega_1$ and $\omega_2$ are two non-zero complex numbers and $a, b$ are non-zero real numbers such that $|a \omega_1 + b \omega_2| = |a \omega_1 - b \omega_2|$,then $\frac{\omega_1}{\omega_2}$ is

$ABCD$ is a rhombus. Its diagonals $AC$ and $BD$ intersect at the point $M$ and satisfy $BD = 2AC$. If the points $D$ and $M$ represent the complex numbers $1 + i$ and $2 - i$ respectively,then $A$ represents the complex number

If $\cos \alpha + \cos \beta + \cos \gamma = 0$ and $\sin \alpha + \sin \beta + \sin \gamma = 0$,then $\cos 2\alpha + \cos 2\beta + \cos 2\gamma = $

The solutions of the equation in $z$,$|z|^2 - (z + \bar{z}) + i(z - \bar{z}) + 2 = 0$ are $(i = \sqrt{-1})$.

$POQ$ is a straight line through the origin $O$. $P$ and $Q$ represent the complex numbers $z_1 = a + ib$ and $z_2 = c + id$ respectively. If $OP = OQ$,then: