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

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

If $|z - 2|/|z - 3| = 2$ represents a circle,then its radius is equal to

$z_1$ and $z_2$ are the roots of $3z^2 + 3z + b = 0$. If the origin,$A(z_1)$,and $B(z_2)$ form an equilateral triangle,then the value of $b$ is equal to

If $|z + 1| = \sqrt{2} |z - 1|$,then the locus described by the point $z$ in the Argand diagram is a

If complex numbers $z_1$ and $z_2$ both satisfy $z + \overline{z} = 2 |z - 1|$ and $\arg(z_1 - z_2) = \frac{\pi}{3},$ then the value of $\text{Im}(z_1 + z_2)$ is,where $\text{Im}(z)$ denotes the imaginary part of $z$.