If $|z_1|=1, |z_2|=2, |z_3|=3$ and $|9z_1z_2 + 4z_1z_3 + z_2z_3| = 12$,then the value of $|z_1 + z_2 + z_3|$ is equal to :-

$ABCD$ 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

Let $a \neq b$ be two non-zero real numbers. Then the number of elements in the set $X = \{ z \in \mathbb{C} : \operatorname{Re}(a z^2 + bz) = a \text{ and } \operatorname{Re}(b z^2 + az) = b \}$ is equal to

The set of points on the Argand plane which satisfy both $|z| \leq 4$ and $\operatorname{Arg}(z) = \frac{\pi}{3}$ represents:

Let $A = \{ z \in \mathbb{C} : |\frac{z+1}{z-1}| < 1 \}$ and $B = \{ z \in \mathbb{C} : \arg(\frac{z-1}{z+1}) = \frac{2\pi}{3} \}$. Then $A \cap B$ is

The region of the Argand plane defined by $|z - 1| + |z + 1| \le 4$ is