If $z_1$ and $z_2$ are two roots of the equation $z^2+az+b=0$ with $a^2 < 4b$, then the origin, $z_1$, and $z_2$ form an equilateral triangle if

Convert the given complex number into polar form: $-3$.

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 least and the largest real values of $\alpha,$ for which the equation $z+\alpha|z-1|+2i=0$ ($z \in \mathbb{C}$ and $i=\sqrt{-1}$) has a solution,are $p$ and $q$ respectively; then $4(p^2+q^2)$ is equal to ..........

If the area of the triangle formed by the points $z, z + iz$ and $iz$ on the complex plane is $18$,then the value of $|z|$ is

$\alpha$ is the real root and $\beta, \gamma$ are the other roots of the equation $x^3-a^3=0$ $(a>0)$. Then the number of common points of the curves given by $|z-\beta|=\frac{\sqrt{3} a}{2}$ and $|z-\gamma|=\frac{\sqrt{3} a}{2}$ is