The value of $|z|^{2}+|z-3|^{2}+|z-i|^{2}$ is minimum when $z$ equals

If $z, \bar{z}, -z, -\bar{z}$ form a rectangle of area $2 \sqrt{3}$ square units,then one such $z$ is

$A$ complex number $z$ is said to be unimodular if $|z| = 1$. Suppose $z_1$ and $z_2$ are complex numbers such that $\frac{z_1 - 2z_2}{2 - z_1 \overline{z_2}}$ is unimodular and $z_2$ is not unimodular. Then the point $z_1$ lies on a:

Let $z$ be a complex number such that the real part of $\frac{z-2i}{z+2i}$ is zero. Then,the maximum value of $|z-(6+8i)|$ is equal to:

If $x + iy = \sqrt{\phi + i\psi}$,where $i = \sqrt{-1}$ and $\phi$ and $\psi$ are non-zero real parameters,then $\phi = \text{constant}$ and $\psi = \text{constant}$ represent two systems of rectangular hyperbolas which intersect at an angle of:

The locus of $z$ satisfying $\left|\frac{z-i}{z-2i}\right|=2$ is a