Let the minimum value $v_{0}$ of $v = |z|^{2} + |z-3|^{2} + |z-6i|^{2}$,where $z \in \mathbb{C}$,be attained at $z = z_{0}$. Then $|2z_{0}^{2} - \bar{z}_{0}^{3} + 3|^{2} + v_{0}^{2}$ is equal to:

Let $z \in \mathbb{C}$ be such that $|z| < 1$. If $w = \frac{5 + 3z}{5(1 - z)}$,then

If $a$ is a complex number and $b$ is a real number,then the equation $\bar{a}+a+b=0$ represents $a$ as a locus of points in the complex plane,which is a:

$PQ$ and $PR$ are two infinite rays. $QAR$ is an arc. $A$ point lying in the shaded region,excluding the boundary,satisfies:

$\alpha$ 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 $z_1 = 2 + 3i$ and $z_2 = 3 + 4i$. The set $S = \{ z \in \mathbb{C} : |z - z_1|^2 - |z - z_2|^2 = |z_1 - z_2|^2 \}$ represents a