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

If $z, iz$ and $z + iz$ are the vertices of a triangle whose area is $2$ units,then the value of $|z|$ is

If $z = x + iy$ and $|z - 2 + i| = |z - 3 - i|$,then the locus of $z$ is:

If $\omega_1$ and $\omega_2$ are two non-zero complex numbers and $a, b$ are non-zero real numbers such that $|a \omega_1 + b \omega_2| = |a \omega_1 - b \omega_2|$,then $\frac{\omega_1}{\omega_2}$ is

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:

If $z = x + iy$ and $|z - zi| = 1,$ then