If $|z_1| = 2$,$|z_2| = 3$,$|z_3| = 4$ and $|2z_1 + 3z_2 + 4z_3| = 9$,then the value of $|8z_2z_3 + 27z_3z_1 + 64z_1z_2|$ is equal to:

The locus of the point $z=x+iy$ satisfying $\left|\frac{z-2i}{z+2i}\right|=1$ is

The inequality $|z - 4| < |z - 2|$ represents the region given by

Let $A$ and $B$ represent $z_1$ and $z_2$ in the Argand plane and $z_1, z_2$ be the roots of the equation $Z^2+pZ+q=0$,where $p, q$ are complex numbers. If $O$ is the origin,$OA=OB$ and $\angle AOB=\alpha$,then $p^2=$

For $z \in \mathbb{C}$,if the minimum value of $(|z-3 \sqrt{2}| + |z-p \sqrt{2} i|)$ is $5 \sqrt{2}$,then a value of $p$ is $.......$

The number of elements in the set $\{ z = a + ib \in \mathbb{C} : a, b \in \mathbb{Z} \text{ and } 1 < |z - 3 + 2i| < 4 \}$ is: