The region represented by $\{z=x+iy \in \mathbb{C} : |z|-\operatorname{Re}(z) \leq 1\}$ is also given by the inequality

$A$ point $z$ moves on the Argand diagram in such a way that $|z - 3i| = 2$. Then its locus will be:

If $z=x+iy$ and if the point $P$ in the Argand plane represents $z$,then the locus of $P$ satisfying the equation $|z-3i|+|z+3i|=10$ is

Let $z_{1}$ be a fixed point on the circle of radius $1$ centered at the origin in the Argand plane and $z_{1} \neq \pm 1$. Consider an equilateral triangle inscribed in the circle with $z_{1}, z_{2}, z_{3}$ as the vertices. Then, $z_{1} z_{2} z_{3}$ is equal to

$A(z_1)$ and $B(z_2)$ are two points in the Argand plane. Then,the locus of the complex number $z$ satisfying $\arg \left(\frac{z-z_1}{z-z_2}\right)=0$ or $\pi$ is

$z=x+iy$ and the point $P$ represents $z$ in the Argand plane. If the amplitude of $\left(\frac{2z-i}{z+2i}\right)$ is $\frac{\pi}{4}$,then the equation of the locus of $P$ is