Let $z_{1}$ and $z_{2}$ be two complex numbers such that $\arg(z_{1}-z_{2})=\frac{\pi}{4}$ and $z_{1}, z_{2}$ satisfy the equation $|z-3|=\operatorname{Re}(z)$. Then the imaginary part of $z_{1}+z_{2}$ is equal to ..... .

If ${z_1}, {z_2}, {z_3}, {z_4}$ are the affixes of four points in the Argand plane and $z$ is the affix of a point such that $|z - z_1| = |z - z_2| = |z - z_3| = |z - z_4|$,then ${z_1}, {z_2}, {z_3}, {z_4}$ are

If $a$ and $b$ are the least and the greatest values respectively of $|z_1+z_2|$,where $z_1=12+5i$ and $|z_2|=9$,then $a^2+b^2=$

If $|z + 4| \le 3$,then the greatest and the least value of $|z + 1|$ are

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:

The locus of the point $z$ satisfying the equation $|iz - 1| + |z - i| = 2$ is