The inequality $|z - 4| < |z - 2|$ represents the region given by

The equation $\overline{b}z + b\overline{z} = c$,where $b$ is a non-zero complex constant and $c$ is real,represents:

The number of elements in the set $\{ z = a + ib \in \mathbb{C} : a, b \in \mathbb{Z} \text{ and } 1 < |z - 3 + 2i| < 4 \}$ 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

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

If $z = x + iy$ is a complex number and $|1 + iz| = |1 - iz|$, then