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

If ${z_1}, {z_2}, {z_3}$ are affixes of the vertices $A, B$ and $C$ respectively of a triangle $ABC$ having centroid at $G$ such that $z = 0$ is the midpoint of $AG$,then:

$A$ function $f$ is defined on the complex numbers by $f(z) = (a + ib)z$,where $a, b \in \mathbb{R}^+$. This function has the property that the $f$-image of any point in the complex plane is equidistant from that point and the origin. If $|a + bi| = 10$ and $b^2 = \frac{p}{q}$,where $p, q \in \mathbb{Z}$ and $\text{gcd}(p, q) = 1$,then $p + q$ is:

The maximum distance from the origin of coordinates to the point $z$ satisfying the equation $\left| z + \frac{1}{z} \right| = a$ is

If $|z|=1$ and $z \neq \pm 1$, then all the points representing $\frac{z}{1-z^{2}}$ lie on;

If $\text{Im} \left( \frac{2z + 1}{iz + 1} \right) = -3$,then the locus of $z$ is :-