If $\frac{z - \alpha}{z + \alpha}$ (where $\alpha \in R$) is a purely imaginary number and $|z| = 2$,then a value of $\alpha$ is

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

Let $S = \{z : 3 \le |2z - 3(1 + i)| \le 7\}$ be a set of complex numbers. Then $\min_{z \in S} |z + \frac{1}{2}(5 + 3i)|$ is equal to:

The region of the Argand plane defined by $|z - 1| + |z + 1| \le 4$ is

If ${z_1}$ and ${z_2}$ are two complex numbers such that $\left| \frac{{z_1} - {z_2}}{{z_1} + {z_2}} \right| = 1$ and $i{z_1} = k{z_2}$,where $k \in R$,then the angle between ${z_1} - {z_2}$ and ${z_1} + {z_2}$ is

If the amplitude of $z-2-3i$ is $\frac{\pi}{4}$,then the locus of $z=x+iy$ is: