The complex numbers $z = x + iy$ which satisfy the equation $\left| \frac{z - 5i}{z + 5i} \right| = 1$ lie on

In the complex plane $\mathbb{C}$,the set $\{z \in \mathbb{C} : \arg \left(\frac{z-1}{z+1}\right) = \frac{\pi}{4}\}$ represents

If $z_{1}=2+3i$ and $z_{2}=3+4i$ are two points on the complex plane, then the set of complex numbers $z$ satisfying $|z-z_{1}|^{2}+|z-z_{2}|^{2}=|z_{1}-z_{2}|^{2}$ represents:

Let $z$ be a complex number such that $|z-6|=5$ and $|z+2-6i|=5$. Then the value of $z^{3}+3z^{2}-15z+141$ is equal to

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:

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