If $|z + 1| = \sqrt{2} |z - 1|$,then the locus described by the point $z$ in the Argand diagram is a

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

The points in the set $\{z \in \mathbb{C} : \arg \left(\frac{z-2}{z-6i}\right) = \frac{\pi}{2}\}$ (where $\mathbb{C}$ denotes the set of all complex numbers) lie on the curve which is a

The locus of a point $z$ in the Argand plane that moves satisfying the equation $|z - (1 - i)| - |z - (2 + i)| = 3$ is:

The region represented by $\{z=x+iy \in \mathbb{C} : |z|-\operatorname{Re}(z) \leq 1\}$ is also given by the inequality

The equation of the locus of $z$ such that $\left|\frac{z-i}{z+i}\right|=2$,where $z=x+iy$ is a complex number,is