The minimum value of $|z-1|+|z-5|$ is

The number of complex numbers $z$ satisfying $|z|=1$ and $\left|\frac{z}{\bar{z}}+\frac{\bar{z}}{z}\right|=1$ is:

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

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:

Let $\left|\frac{\bar{z}-i}{2 \bar{z}+i}\right|=\frac{1}{3}$,where $z \in \mathbb{C}$,be the equation of a circle with center at $C$. If the area of the triangle,whose vertices are at the points $(0,0)$,$C$,and $(\alpha, 0)$,is $11$ square units,then $\alpha^2$ equals

If $z$ is a complex number such that $z^2 = (\bar{z})^2$,then