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

The locus of $z=x+iy$, such that $\operatorname{Im}\left(\frac{z-3i}{iz+4}\right)=0$ is

Let $S = \{z = x + iy : \frac{2z - 3i}{4z + 2i} \text{ is a real number} \}$. Then which of the following is $NOT$ correct?

Let $A_1, A_2, A_3, \ldots, A_8$ be the vertices of a regular octagon that lie on a circle of radius $2$. Let $P$ be a point on the circle and let $PA_i$ denote the distance between the points $P$ and $A_i$ for $i=1, 2, \ldots, 8$. If $P$ varies over the circle,then the maximum value of the product $PA_1 \cdot PA_2 \cdot \cdots \cdot PA_8$ is:

If $A, B, C$ are represented by $3 + 4i, 5 - 2i, -1 + 16i$,then $A, B, C$ are

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