If $z$ is any complex number satisfying $|z - 3 - 2i| \leq 2$,then the minimum value of $|2z - 6 + 5i|$ is

The equation $z \bar{z} + (2 - 3i) z + (2 + 3i) \bar{z} + 4 = 0$ represents a circle of radius (in $\text{ units}$)

If $z_{1}=2+3i$ and $z_{2}=3+4i$ are two points on the complex plane, then the set of complex numbers $z$ satisfying $|z-z_{1}|^{2}+|z-z_{2}|^{2}=|z_{1}-z_{2}|^{2}$ represents:

The points representing the complex number $z$ for which $\text{arg}\left(\frac{z-2}{z+2}\right)=\frac{\pi}{3}$ lie on

$\alpha$ is the real root and $\beta, \gamma$ are the other roots of the equation $x^3-a^3=0$ $(a>0)$. Then the number of common points of the curves given by $|z-\beta|=\frac{\sqrt{3} a}{2}$ and $|z-\gamma|=\frac{\sqrt{3} a}{2}$ is

Let $A = \{z \in \mathbb{C} : 1 \leq |z - (1 + i)| \leq 2\}$ and $B = \{z \in A : |z - (1 - i)| = 1\}$. Then,$B$ is: