If $z$ is a complex number such that $\frac{z - 1}{z + 1}$ is purely imaginary,then

If $z = x + iy$ represents a point in the Argand plane,then a point which is not in the region represented by $|z - 1 + i| \leq 2$ is

Let $\left|\frac{\bar{z}-i}{2 \bar{z}+i}\right|=\frac{1}{3}$,where $z \in \mathbb{C}$,be the equation of a circle with center at $C$. If the area of the triangle,whose vertices are at the points $(0,0)$,$C$,and $(\alpha, 0)$,is $11$ square units,then $\alpha^2$ equals

If $m$ and $n$ are the least and greatest values of $|z|$ respectively and $|z-4+3 i| \leq 1$. Let $k$ be the least value of $\frac{x^4+x^2+4}{x}$ on the interval $(0, \infty)$. Then $k=$

If the point $\left(\frac{k-1}{k}, \frac{k-2}{k}\right)$ lies on the locus of $z$ satisfying the inequality $\left|\frac{z+3i}{3z+i}\right| < 1$,then the interval in which $k$ lies is

If $z$ is a complex number satisfying $|z - 3| \leq 5$,then the range of $|z + 3i|$ is (where $i = \sqrt{-1}$).