If the center and radius of the circle $\left|\frac{z-2}{z-3}\right|=2$ are respectively $(\alpha, \beta)$ and $\gamma$,then $3(\alpha+\beta+\gamma)$ is equal to

If $\omega$ is a complex cube root of unity whose imaginary part is positive and $|z - \omega| = |z + \omega|$,then $arg(z)$ can be-

$S = \{z \in \mathbb{C} : |z - 1 + i| = 1\}$ represents

Let ${z_1}, {z_2}, {z_3}$ be three vertices of an equilateral triangle circumscribing the circle $|z| = \frac{1}{2}$. If ${z_1} = \frac{1}{2} + \frac{\sqrt{3}i}{2}$ and ${z_1}, {z_2}, {z_3}$ are in anticlockwise sense,then ${z_2}$ is

If $a$ is a complex number and $b$ is a real number,then the equation $\bar{a}+a+b=0$ represents $a$ as a:

If $z$ is a complex number,then the curves $|z|=1$,$|z-2|=1$,and $|z-1|=0$ have a common point at