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 $|z-3 i|+|z+5 i|=4$,then the locus of $z$ is

If $z=x+iy, x, y \in R$ and the imaginary part of $\frac{\bar{z}-1}{\bar{z}-i}$ is $1$,then the locus of $z$ is

Let the point $P$ represent $z=x+iy$, where $x, y \in \mathbb{R}$, in the Argand plane. Let the curves $C_1$ and $C_2$ be the loci of $P$ satisfying the conditions $(i)$ $\frac{2z+i}{z-2}$ is purely imaginary and $(ii)$ $\operatorname{Arg}\left(\frac{z+i}{z+1}\right)=\frac{\pi}{2}$, respectively. Then the point of intersection of the curves $C_1$ and $C_2$, other than the origin, is

The number of solutions of the equation $z^{2}+\overline{z}=0$,where $z \in \mathbb{C}$,is

If $z$ is a complex number having the least absolute value and $|z - 2 + 2i| = 1$,then $z =$