List of top Mathematics Questions on argand plane asked in AP EAPCET

If the point \(P\) represents a complex number \(z\) in the Argand diagram and \[ \frac{z-i}{z-1} \] is always purely imaginary, then the locus of \(P\) is

The locus of a point \(z\) satisfying \[ |z|^2=\operatorname{Re}(z) \] is a circle with centre