If $z = x + iy$ and $|z - 2 + i| = |z - 3 - i|$,then the locus of $z$ is:

The number of points $z$ on the Argand plane which satisfy the conditions $\operatorname{Re}\left(\frac{z-2}{z-4i}\right)=0$ and $\operatorname{Im}\left(\frac{z-2}{z-4i}\right)=1$ simultaneously is

Let $S_{1}=\{z_{1} \in \mathbb{C}:|z_{1}-3|=\frac{1}{2}\}$ and $S_{2}=\{z_{2} \in \mathbb{C}:|z_{2}-|z_{2}+1||=|z_{2}+|z_{2}-1||\}$. Then,for $z_{1} \in S_{1}$ and $z_{2} \in S_{2}$,the least value of $|z_{2}-z_{1}|$ is:

If $z = x + iy$ and $|z - zi| = 1,$ then

Let $z = x + iy$ be a point in the Argand plane. If the amplitude of $\left(\frac{z - 3}{z + 2i}\right)$ is $\frac{\pi}{2}$,then the locus of $z$ is

Let $z=x+iy$ be a complex number,where $x$ and $y$ are integers and $i=\sqrt{-1}$. Then the area of the rectangle whose vertices are the roots of the equation $z\bar{z}^3+\bar{z}z^3=350$ is