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

Let $z \in \mathbb{C}$ be such that $|z| < 1$. If $w = \frac{5 + 3z}{5(1 - z)}$,then

The locus of the points $z$ which satisfy the condition $\text{arg} \left( \frac{z - 1}{z + 1} \right) = \frac{\pi}{3}$ is

If $|z + 1| = \sqrt{2} |z - 1|$,then the locus described by the point $z$ in the Argand diagram is a

Let $C$ be the circle in the complex plane with centre $z_0 = \frac{1}{2}(1 + 3i)$ and radius $r = 1$. Let $z_1 = 1 + i$ and the complex number $z_2$ be outside the circle $C$ such that $|z_1 - z_0| |z_2 - z_0| = 1$. If $z_0, z_1$ and $z_2$ are collinear,then the smaller value of $|z_2|^2$ is equal to $.............$.

The complex number $\frac{1 + 2i}{1 - i}$ lies in which quadrant of the complex plane?