If $|Z_1|=|Z_2|=|Z_3|=1$ and $Z_1+Z_2+Z_3=0$, then the area of the triangle whose vertices are $Z_1, Z_2, Z_3$ is

$ABCD$ is a rhombus. Its diagonals $AC$ and $BD$ intersect at the point $M$ and satisfy $BD = 2AC$. If the points $D$ and $M$ represent the complex numbers $1 + i$ and $2 - i$ respectively,then $A$ represents the complex number

The value of $|z|^{2}+|z-3|^{2}+|z-i|^{2}$ is minimum when $z$ equals

If $\left| \frac{z - 1}{z - 4} \right| = 2$ and $\left| \frac{w - 4}{w - 1} \right| = 2$,then the value of $|z - w|_{\max} + |z - w|_{\min}$ is

If $C$ is a point on the straight line joining the points $A(-2+i)$ and $B(3-4i)$ in the Argand plane and $\frac{AC}{CB}=\frac{1}{2}$,then the argument of $C$ is

The sum of the square of the modulus of the elements in the set $\{z=a+ib: a, b \in \mathbb{Z}, z \in \mathbb{C}, |z-1| \leq 1, |z-5| \leq |z-5i|\}$ is ........