If the points $P_1$ and $P_2$ represent two complex numbers $z_1$ and $z_2$ respectively,then the point $P_3$ represents the number

If $z, iz$ and $z+iz$ are the vertices of a triangle and if $|z|=4$,then the area (in sq. units) of that triangle is:

If the center and radius of the circle $\left|\frac{z-2}{z-3}\right|=2$ are respectively $(\alpha, \beta)$ and $\gamma$,then $3(\alpha+\beta+\gamma)$ is equal to

The largest value of $r$ for which the region represented by the set $\{ \omega \in \mathbb{C} : |\omega - 4 - i| \le r \}$ is contained in the region represented by the set $\{ z \in \mathbb{C} : |z - 1| \le |z + i| \}$ is equal to

The complex numbers $z_1, z_2$ and $z_3$ satisfying $\frac{z_1 - z_3}{z_2 - z_3} = \frac{1 - i\sqrt{3}}{2}$ are the vertices of a triangle which is

$PQ$ and $PR$ are two infinite rays. $QAR$ is an arc. $A$ point lying in the shaded region,excluding the boundary,satisfies: