If $\frac{|3z - i|}{|4z - 2 + 3i|} = K$ $(K \in \mathbb{R}^+)$ represents a straight line,then the value of $K$ is:

The vertices $B$ and $D$ of a parallelogram are $1 - 2i$ and $4 + 2i$. If the diagonals are at right angles and $AC = 2BD$,the complex number representing $A$ is

The area of the triangle whose vertices are complex numbers $z, iz, z + iz$ in the Argand diagram is

Let $S$ be the set of all complex numbers $z$ satisfying $|z-2+i| \geq \sqrt{5}$. If the complex number $z_0$ is such that $\frac{1}{|z_0-1|}$ is the maximum of the set $\left\{\frac{1}{|z-1|}: z \in S\right\}$,then the principal argument of $\frac{4-z_0-\bar{z}_0}{z_0-\bar{z}_0+2i}$ is

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

If $P(x, y)$ denotes $z = x + iy$ where $x, y \in \mathbb{R}$ and $i = \sqrt{-1}$ in the Argand plane,and $\left|\frac{z-1}{z+2i}\right| = 1$,then the locus of $P$ is