List of top Mathematics Questions on argand plane

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

If \[ z=\frac{(1-i)^2}{(-\sqrt3+i)^3}, \] then the principal amplitude of \(z\) is

If \[ z=(\sqrt3-i)^{2025}+(-1-\sqrt3 i)^{2026}, \] then the point corresponding to \(z\) in the Argand plane lies in

If \[ \arg\left(\frac{z-1}{z+1}\right)=\frac{\pi}{4}, \] then the locus of the point \(P(z)\) on the Argand plane is a

All the points in $A=\{\frac{\lambda+i}{\lambda-i}; \lambda \in \mathbb{R}\}$ lie on ________.

The points represented by the complex numbers \( 1 + i, -2 + 3i, \frac{5}{3}i \) on the Argand plane are:

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

The points represented by the complex numbers \[ 1 + i, \quad -2 + 3i, \quad \frac{5}{3} i \] on the Argand plane are: