If $|z - 3i| \le 5$,then the minimum value of $|z + 2|$ is equal to

If $|z| = 1$ $(z \neq -1)$ and $z = x + iy$,then $\left( \frac{z - 1}{z + 1} \right)$ is

Let $z_{1}$ be a fixed point on the circle of radius $1$ centered at the origin in the Argand plane and $z_{1} \neq \pm 1$. Consider an equilateral triangle inscribed in the circle with $z_{1}, z_{2}, z_{3}$ as the vertices. Then,$z_{1} z_{2} z_{3}$ is equal to

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

If $z_1$ and $z_2$ are two roots of the equation $z^2+az+b=0$ with $a^2 < 4b$,then the origin,$z_1$,and $z_2$ form an equilateral triangle if

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