If $z = x + iy$ is a complex number and $|1 + iz| = |1 - iz|$, then

If the roots of the equation $Z^3+i Z^2+2 i=0$ are the vertices of a triangle $ABC$,then that triangle $ABC$ is

If the locus of $z \in \mathbb{C}$, such that $\operatorname{Re}\left(\frac{z-1}{2 z+i}\right)+\operatorname{Re}\left(\frac{\bar{z}-1}{2 \bar{z}-i}\right)=2$, is a circle of radius $r$ and center $(a, b)$, then $\frac{15 a b}{r^2}$ is equal to :

Let $z = x + iy$ be a non-zero complex number such that $z^{2} = i|z|^{2},$ where $i = \sqrt{-1}.$ Then $z$ lies on the:

Let ${z_1}, {z_2}, {z_3}$ be three vertices of an equilateral triangle circumscribing the circle $|z| = \frac{1}{2}$. If ${z_1} = \frac{1}{2} + \frac{\sqrt{3}i}{2}$ and ${z_1}, {z_2}, {z_3}$ are in anticlockwise sense,then ${z_2}$ is

Let $a = \text{Im}\left( \frac{1 + z^2}{2iz} \right)$,where $z$ is any non-zero complex number. The set $A = \{ a : |z| = 1 \text{ and } z \ne \pm 1 \}$ is equal to