The locus of $z$ satisfying $|z|+|z-1|=3$ is

If $z, iz$ and $z + iz$ are the vertices of a triangle whose area is $2$ units,then the value of $|z|$ is

Let $z=x+yi$,where $x, y$ are integers and $i=\sqrt{-1}$. The area of the rectangle whose vertices are the roots of the equation $\bar{z}z^3+z(\bar{z})^3=700$ is

The locus of $z$ satisfying $\left|\frac{z-i}{z-2i}\right|=2$ is a

If $z=x+iy$,then the equation $|z+1|=|z-1|$ represents

Let $w = \frac{\sqrt{3} + i}{2}$ and $P = \{w^n : n = 1, 2, 3, \ldots\}$. Further, $H_1 = \{z \in C : \operatorname{Re}(z) > \frac{1}{2}\}$ and $H_2 = \{z \in C : \operatorname{Re}(z) < -\frac{1}{2}\}$, where $C$ is the set of all complex numbers. If $z_1 \in P \cap H_1$, $z_2 \in P \cap H_2$, and $O$ represents the origin, then $\angle z_1 O z_2$ can be: