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

If $|z + 4| \le 3$,then the greatest and the least value of $|z + 1|$ are

Let $A, B, C$ be three sets of complex numbers as defined below:
$A = \{z : \operatorname{Im}(z) \geq 1\}$
$B = \{z : |z - 2 - i| = 3\}$
$C = \{z : \operatorname{Re}((1 - i)z) = \sqrt{2}\}$
$1.$ The number of elements in the set $A \cap B \cap C$ is:
$(A) 0, (B) 1, (C) 2, (D) \infty$
$2.$ Let $z$ be any point in $A \cap B \cap C$. Then,$|z + 1 - i|^2 + |z - 5 - i|^2$ lies between:
$(A) 25 \text{ and } 29, (B) 30 \text{ and } 34, (C) 35 \text{ and } 39, (D) 40 \text{ and } 44$
$3.$ Let $z$ be any point in $A \cap B \cap C$ and let $w$ be any point satisfying $|w - 2 - i| < 3$. Then,$|z| - |w| + 3$ lies between:
$(A) -6 \text{ and } 3, (B) -3 \text{ and } 6, (C) -6 \text{ and } 6, (D) -3 \text{ and } 9$

Let $X_{n} = \{z = x + iy : |z|^{2} \leq \frac{1}{n}\}$ for all integers $n \geq 1$. Then, $\bigcap_{n=1}^{\infty} X_{n}$ is

If $z=x+iy$ represents a point $P$ in the Argand plane, then the area of the region represented by the inequality $2 < |z-(1+i)| < 3$ is (in $\pi$)

If $a$ and $c$ are complex numbers and $b$ is a real number in the Argand plane,then the perpendicular distance from $c$ to the line $a \bar{z} + \bar{a} z + b = 0$ is