In the Argand plane,the values of $z$ satisfying the equation $|z-1|=|i(z+1)|$ lie on

Let $z_{1}$ be a fixed point on the circle of radius $1$ centered at the origin in the Argand plane and $z_{1} \neq \pm 1$. Consider an equilateral triangle inscribed in the circle with $z_{1}, z_{2}, z_{3}$ as the vertices. Then,$z_{1} z_{2} z_{3}$ is equal to

The locus represented by $|z - 1| = |z + i|$ is

If $|z_1 + z_2| = |z_1 - z_2|$,then the difference in the amplitudes of $z_1$ and $z_2$ is

If the equation $a|z|^2 + \overline{\bar{\alpha}z + \alpha\bar{z}} + d = 0$ represents a circle where $a, d$ are real constants,then which of the following conditions is correct?

In the Argand plane,the vector $z = 4 - 3i$ is turned in the clockwise sense through $180^o$ and stretched three times. The complex number represented by the new vector is