If the complex numbers $z_1, z_2, 0$ are vertices of an equilateral triangle,then $z_1^2 + z_2^2 =$

The reflection of the complex number $(3 + 2i)$ in the straight line $z = -i \bar{z}$ is-

Which of the following equations can represent a triangle in the complex plane?

Let the complex numbers $z_1, z_2$ and $z_3$ be the vertices of an equilateral triangle. Let $z_0$ be the circumcentre of the triangle,then $z_1^2 + z_2^2 + z_3^2 = $

Let $a$ be a complex number such that $|a| < 1$ and $z_1, z_2, \dots$ be vertices of a polygon such that $z_k = 1 + a + a^2 + \dots + a^{k-1}$. Then the vertices of the polygon lie within a circle:

If $Z$ is a complex number such that $|Z| \leq 3$ and $-\frac{\pi}{2} \leq \operatorname{amp}(Z) \leq \frac{\pi}{2}$,then the area of the region formed by the locus of $Z$ is