If a complex number $z$ is such that $\frac{z-2 i}{z-2}$ is purely imaginary number and the locus of $z$ is a closed curve, then the area of the region bounded by that closed curve and lying in the first quadrant is $\frac{z-2 i}{z-2}$

Real part of $\frac{(\cos a+i \sin a)^6}{(\sin b+i \cos b)^8}$ is

If real parts of $\sqrt{-5-12 i}, \sqrt{5+12 i}$ are positive values, the real part of $\sqrt{-8-6 i}$ is a negative value and $a+i b=\frac{\sqrt{-5-12 i}+\sqrt{5+12 i}}{\sqrt{-8-6 i}}$, then $2 a+b=$

The set of all real values of $ c $ for which the equation $ z\overline{z} + (4 - 3i)z + (4 + 3i)\overline{z} + c = 0 $ represents a circle, is