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

Let $z_{1}$ and $z_{2}$ be two fixed complex numbers in the Argand plane and $z$ be an arbitrary point satisfying $|z-z_{1}|+|z-z_{2}|=2|z_{1}-z_{2}|$. Then, the locus of $z$ will be

Let $S = \{z \in \mathbb{C} : z^{2} + \bar{z} = 0\}$. Then $\sum_{z \in S} (\operatorname{Re}(z) + \operatorname{Im}(z))$ is equal to $......$

If $|Z_1|=|Z_2|=|Z_3|=1$ and $Z_1+Z_2+Z_3=0$, then the area of the triangle whose vertices are $Z_1, Z_2, Z_3$ is

Let $S = \{z = x + iy : |z - 1 + i| \geq |z|, |z| < 2, |z + i| = |z - 1|\}$. Then the set of all values of $x$,for which $w = 2x + iy \in S$ for some $y \in \mathbb{R}$,is:

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