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

If the point $P$ denotes the complex number $z=x+iy$ in the Argand plane and $\frac{z-(2-i)}{z+(1+2i)}$ is a purely imaginary number,then the locus of $P$ is

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

If $z_1$ and $z_2$ are two distinct complex numbers such that $\left|\frac{z_1-2 z_2}{\frac{1}{2}-z_1 \bar{z}_2}\right|=2$,then:

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

The equation $|z+1-i|=|z-1+i|$ represents a (where $z$ is a complex number)