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

Let $w_1$ be the point obtained by the rotation of $z_1=5+4i$ about the origin through a right angle in the anticlockwise direction,and $w_2$ be the point obtained by the rotation of $z_2=3+5i$ about the origin through a right angle in the clockwise direction. Then the principal argument of $w_1-w_2$ is equal to $...........$.

If $z = x + iy$ and $\omega = \frac{1 - iz}{z - i}$,then $|\omega| = 1$ shows that in the complex plane:

If $A, B, C$ are represented by $3 + 4i, 5 - 2i, -1 + 16i$,then $A, B, C$ are

Let $C$ be the set of all complex numbers. Let $S_{1} = \{z \in C : |z-3-2i|^{2}=8\}$,$S_{2} = \{z \in C : \operatorname{Re}(z) \geq 5\}$,and $S_{3} = \{z \in C : |z-\bar{z}| \geq 8\}$. Then the number of elements in $S_{1} \cap S_{2} \cap S_{3}$ is equal to:

Let $A(3-i)$ and $B(2+i)$ be two points in the Argand plane. If the point $P$ represents the complex number $z=x+iy$,which satisfies $|z-3+i|=|z-2-i|$,then the locus of the point $P$ is