If $|z + 4| \le 3$,then the maximum value of $|z + 1|$ is

Let $z_1, z_2 \in \mathbb{C}$ such that $|z_1 + z_2| = \sqrt{3}$ and $|z_1| = |z_2| = 1$. Then the value of $|z_1 - z_2|$ is

If the amplitude of $z-2-3i$ is $\pi/4$,then the locus of $z=x+iy$ is

If $w = \frac{z}{z - \frac{1}{3}i}$ and $|w| = 1$,then $z$ lies on

Let $S = \{z \in \mathbb{C} - \{i, 2i\} : \frac{z^2 + 8iz - 15}{z^2 - 3iz - 2} \in \mathbb{R} \}$. If $\alpha - \frac{13}{11}i \in S$ and $\alpha \in \mathbb{R} - \{0\}$,then $242\alpha^2$ is equal to

If the equation $a|z|^2 + \overline{\bar{\alpha}z + \alpha\bar{z}} + d = 0$ represents a circle where $a, d$ are real constants,then which of the following conditions is correct?