$|{z_1} + {z_2}| = |{z_1}| + |{z_2}|$ is possible if

If $|z - 3 + 2i| \leq 4$,then the difference between the greatest value and the least value of $|z|$ is

Let $C$ be the set of all complex numbers. Let $S_{1} = \{z \in C : |z-3-2i|^{2}=8\}$,$S_{2} = \{z \in C : \operatorname{Re}(z) \geq 5\}$,and $S_{3} = \{z \in C : |z-\bar{z}| \geq 8\}$. Then the number of elements in $S_{1} \cap S_{2} \cap S_{3}$ is equal to:

If the complex numbers $z_1, z_2, 0$ are vertices of an equilateral triangle,then $z_1^2 + z_2^2 =$

If a point $P$ denotes the complex number $z=x+iy$ in the Argand plane and if $\frac{z-(2+i)}{z+(1-2i)}$ is purely real,then the locus of $P$ is

The locus of $z$ satisfying $|z|+|z-1|=3$ is