Let $z=x+iy$ and a point $P$ represent $z$ in the Argand plane. If the real part of $\frac{z-1}{z+i}$ is $1$,then a point that lies on the locus of $P$ is

If the amplitude of $(Z-2)$ is $\frac{\pi}{2}$,then the locus of $Z$ is:

$\alpha$ 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

If $P, Q, R, S$ are represented by the complex numbers $4 + i, 1 + 6i, -4 + 3i, -1 - 2i$ respectively,then $PQRS$ is a

If a complex number $z = x + iy$ is taken such that the amplitude of the fraction $\frac{z - 1}{z + 1}$ is always $\frac{\pi}{4}$,then:

If $|z| = 2$,then the points representing the complex numbers $-1 + 5z$ will lie on a