List of top Mathematics Questions on argand plane

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

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

The number of the distinct real roots of the equation $\begin{vmatrix}\sin x&\cos x&\cos x\\ \cos x&\sin x&\cos x\\ \cos x&\cos x&\sin x\end{vmatrix} = 0 $ , in the interval $ - \frac{\pi}{4} \le x \le \frac{\pi}{4}$ is

If $\alpha, \beta$ and $\gamma$ are the roots of the equation $x^3 - 3x^2 + 3x + 7 = 0$, and w is cube root of unity, then the value of $\frac{\alpha-1}{\beta-1} + \frac{\beta-1}{\gamma-1} + \frac{\gamma-1}{\alpha-1}$ is equal to

The perimeter of the locus represented by arg $\left( \frac{z + i}{z-i}\right) = \frac{\pi}{4}$ is equal to

The number of real roots of the equation $e^{x-1} + x - 2 = 0$ is

Suppose $z = x + iy$ where $x$ and $y$ are real numbers and $i = \sqrt{-1}$. The points $(x, y)$ for which $\frac{z - 1}{z - i} $ is real, lie on

If $z=\frac{1-i \sqrt{3}}{1+i \sqrt{3}}$, then $\arg (z)$ is

The amplitude of $(1+i)^5$ is

The amplitude of $\sin \frac{\pi}{5} + i\left( 1 - \cos \frac{\pi}{5}\right) $

If $0 < \alpha

If $z= x +iy , x,y \in R , (x,y) \ne (0, -4)$ and $Arg \left( \frac{2z-3}{z+4i}\right) = \frac{\pi}{4}$ , then the locus of $z$ is

If $z = x + iy , x , y \in R$ and the imaginary part of $\frac{\bar{z} - 1}{\bar{z} - i}$ is $1$ then the locus of $z$ is

The points $ 0, 2 + 3i, i, - 2 - 2i $ in the argand plane are the vertices of a

Suppose $z_1, z_2, z_3$ are the vertices of an equilateral triangle inscribed in the circle $| z| = 2$. If $z_1$ = $\sqrt {3i}$ and $z_1,z_2,z_3$ are in . the clockwise sense, then