If $|z - 2 - 3i| + |z + 2 - 6i| = 4$,where $i = \sqrt{-1}$,then the locus of $P(z)$ is

For any complex number $z$, the minimum value of $|z| + |z - 1|$ is

The maximum value of $|z|$ where $z$ satisfies the condition $\left| z + \frac{2}{z} \right| = 2$ is

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:

Let $S_{1}, S_{2}$ and $S_{3}$ be three sets defined as:
$S_{1} = \{ z \in C : |z - 1| \leq \sqrt{2} \}$
$S_{2} = \{ z \in C : \operatorname{Re}((1 - i)z) \geq 1 \}$
$S_{3} = \{ z \in C : \operatorname{Im}(z) \leq 1 \}$
Then the set $S_{1} \cap S_{2} \cap S_{3}$

If $\cos \alpha + \cos \beta + \cos \gamma = 0$ and $\sin \alpha + \sin \beta + \sin \gamma = 0$,then $\cos 2\alpha + \cos 2\beta + \cos 2\gamma = $