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:

Reflection of the line $\bar{a} z+a \bar{z}=0$ in the real axis is given by

If $z_1$ and $z_2$ are two distinct complex numbers such that $\left|\frac{z_1-2 z_2}{\frac{1}{2}-z_1 \bar{z}_2}\right|=2$,then:

Let $S_1 = \{z \in \mathbb{C} : |z| \leq 5\}$, $S_2 = \{z \in \mathbb{C} : \operatorname{Im}\left(\frac{z+1-\sqrt{3}i}{1-\sqrt{3}i}\right) \geq 0\}$ and $S_3 = \{z \in \mathbb{C} : \operatorname{Re}(z) \geq 0\}$. Then the area of the region $S_1 \cap S_2 \cap S_3$ is:

Let $O$ be the origin,the point $A$ be $z_1 = \sqrt{3} + 2\sqrt{2}i$,and the point $B(z_2)$ be such that $\sqrt{3}|z_2| = |z_1|$ and $\arg(z_2) = \arg(z_1) + \frac{\pi}{6}$. Then:

Let $z=x+iy$ represent a point $P(x, y)$ in the Argand plane. If $z$ satisfies the condition that $\text{arg}\left(\frac{z-3}{z-2i}\right)=-\frac{\pi}{2}$,then the locus of $P$ is