If $\text{Im} \left( \frac{2z + 1}{iz + 1} \right) = -3$,then the locus of $z$ is :-

$\sinh(ix)$ is equal to:

If $z$ and $\omega$ are two non-zero complex numbers such that $|z \omega|=1$ and $\operatorname{Arg}(z) - \operatorname{Arg}(\omega) = \frac{\pi}{2}$,then $\bar{z} \omega =$

If ${z_1}$ and ${z_2}$ are two complex numbers satisfying the equation $\left| \frac{z_1 + z_2}{z_1 - z_2} \right| = 1$,then $\frac{z_1}{z_2}$ is a number which is

$z_1$ and $z_2$ are the roots of $3z^2 + 3z + b = 0$. If the origin,$A(z_1)$,and $B(z_2)$ form an equilateral triangle,then the value of $b$ is equal to

If a complex number $z$ satisfies $|z^2-1|=|z|^2+1$,then $z$ lies on