The solutions of equation in $z$, $| z |^2 -(z + \bar{z}) + i(z - \bar{z})$ + $2$ = $0$ are $(i = \sqrt{-1})$

The inequality $|z - 4|\, < \,|\,z - 2|$represents the region given by

The maximum value of $|z|$ where z satisfies the condition $\left| {z + \frac{2}{z}} \right| = 2$ is

Find the modulus and argument of the complex number $\frac{1+2 i}{1-3 i}$

If $z$ is a complex number, then the minimum value of $|z| + |z - 1|$ is

The complex numbers $sin\ x + i\ cos\ 2x$ and $cos\ x\ -\ i\ sin\ 2x$ are conjugate to each other, for