If the amplitude of $(z-2-3i)$ is $\frac{3\pi}{4}$,then the locus of $z$ is (where $z=x+iy$):

The locus of $z$ satisfying the inequality $\left|\frac{z+2 i}{2 z+i}\right| < 1$,where $z=x+i y$,is

If $|8 + z| + |z - 8| = 16$,where $z$ is a complex number,then the point $z$ will lie on

Let $z_1$ and $z_2$ be two complex numbers and roots of the equation $z^2 + az + b = 0$. If $O$ is the origin such that $OA = OB$ and $a^2 = \lambda b \cos^2 \frac{\alpha}{2}$,where $\alpha$ is the angle $\angle AOB$,then $\lambda$ is equal to:

$S = \{z \in \mathbb{C} : |z - 1 + i| = 1\}$ represents

If $z$ is a complex number such that $z^2 = (\bar{z})^2$,then