Let $z$ be the complex number satisfying $|z-5| \le 3$ and having the maximum positive principal argument. Then $34|\frac{5z-12}{5iz+16}|^{2}$ is equal to:

All the points in the set $S = \left\{ \frac{\alpha + i}{\alpha - i} : \alpha \in R \right\} (i = \sqrt{-1})$ lie on a

Let $S = \{z = x + iy : |z - 1 + i| \geq |z|, |z| < 2, |z + i| = |z - 1|\}$. Then the set of all values of $x$,for which $w = 2x + iy \in S$ for some $y \in \mathbb{R}$,is:

If $z=x+iy$ represents a point $P$ in the Argand plane, then the area of the region represented by the inequality $2 < |z-(1+i)| < 3$ is (in $\pi$)

The locus of the points represented by $|z+3|-|z-3|=6$,where $z$ is a complex number,is ....

If a complex number $z=x+iy$ represents a point $P$ on the Argand plane and $\operatorname{Arg}\left(\frac{z-(3-2i)}{z-(-2+3i)}\right)=\frac{\pi}{4}$,then the locus of $P$ is a