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

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

The region of the complex plane for which $\left| \frac{z - a}{z + \overline{a}} \right| = 1$ where $\text{Re}(a) \neq 0$ is

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 $A = \{z = x + iy : \text{real part of } \frac{\bar{z}-1}{z-i} = 2\}$,then the locus of the point $P(x, y)$ in the Cartesian plane is:

If $|z_1+z_2|^2=|z_1|^2+|z_2|^2$,where $z_1$ and $z_2$ are two complex numbers,then