The locus of $z$ given by $\left| \frac{z - 1}{z - i} \right| = 1$ is

Let $z \in \mathbb{C}$ be a complex number. The equation $2|z + 3i| - |z - i| = 0$ represents:

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

If $z_1 = 1 + 2i$,$z_2 = 2 + 3i$,and $z_3 = 3 + 4i$,then $z_1, z_2, z_3$ represent the vertices of a/an:

$\alpha$ is the real root and $\beta, \gamma$ are the other roots of the equation $x^3-a^3=0$ $(a>0)$. Then the number of common points of the curves given by $|z-\beta|=\frac{\sqrt{3} a}{2}$ and $|z-\gamma|=\frac{\sqrt{3} a}{2}$ is

The locus of $z$ satisfying $|z|+|z-1|=3$ is