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

The locus of $z$ given by $\left| \frac{z - 1}{z - i} \right| = 1$ is

Let $S = \{z \in \mathbb{C} : 4z^2 + \overline{z} = 0\}$. Then $\sum_{z \in S} |z|^2$ 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 $z$ is a complex number such that $\frac{z-i}{z-1}$ is purely imaginary,then the minimum value of $|z-(3+3i)|$ is:

If $\left| z - \frac{1 + 3i}{2} \right| = \frac{\sqrt{10}}{2}$ and $P$,$Q$,and $R$ are points representing the complex numbers $z$,$z e^{i \pi / 3}$,and $z(1 + e^{i \pi / 3})$ respectively in the Argand plane,then the area of the triangle $PQR$ is: