Geometrically,the set $\{z \in \mathbb{C} : |z - 2 - 2i| \leq 1\}$ represents

Let $R$ denote the set of all real numbers. Let $z_1 = 1 + 2i$ and $z_2 = 3i$ be two complex numbers,where $i = \sqrt{-1}$. Let $S = \{(x, y) \in R \times R : |x + iy - z_1| = 2|x + iy - z_2|\}$. Then which of the following statements is (are) True?
$(A) S$ is a circle with centre $\left(-\frac{1}{3}, \frac{10}{3}\right)$
$(B) S$ is a circle with centre $\left(\frac{1}{3}, \frac{8}{3}\right)$
$(C) S$ is a circle with radius $\frac{\sqrt{2}}{3}$
$(D) S$ is a circle with radius $\frac{2\sqrt{2}}{3}$

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

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 $\mu = \frac{2z + 5i}{z - 3}$ and $|\mu| = 2$,then the locus of $z$ is:

If $z = x + iy$ and $|z - 2 + i| = |z - 3 - i|$,then the locus of $z$ is: