List of top Mathematics Questions on Complex numbers asked in VITEEE

Let \( z \neq 1 \) be a complex number and let \( \omega = x + iy, y \neq 0 \). If \[ \frac{\omega -\overline{\omega}z}{1 -z} \] is purely real, then \( |z| \) is equal to

The number of students who take both the subjects mathematics and chemistry is 30. This represents 10% of the enrolment in mathematics and 12% of the enrolment in chemistry. How many students take at least one of these two subjects?

The shortest distance between the lines \( x = y + 2 \), \( z = 6x - 6 \) and \( x + 1 = 2y = -12z \) is:

The equations \( 2x + 3y + 4 = 0 \), \( 3x + 4y + 6 = 0 \), and \( 4x + 5y + 8 = 0 \) are:

If \( \omega = \frac{-1 + \sqrt{3}i}{2} \), then \( (3 + \omega + 3\omega^2) \) is:

If \( z = x + iy \), \( z^{1/3} = a - ib \), then \( \frac{x}{a} = \frac{y}{b} = k \) is equal to:

One of the values of \[ \left( \frac{1 + i}{\sqrt{2}} \right)^{2/3} \] is:

Amplitude of \( \frac{1 + \sqrt{3}i}{\sqrt{3} + 1} \) is:

Amplitude of $\frac{1+\sqrt{3}i}{\sqrt{3}+1}$ is :

The equation \( z^2 + (2 - 3i)z + (2 + 3i) = 4 = 0 \) represents a circle of radius

The value of \( (1 + \omega)^3 \), where \( \omega = e^{i 2\pi/3} \) is

The value of $ (1 + \omega - \omega^2)^7$ is

The value of $ (1 + \omega - \omega^2)^7$ is

If $|z| \ge 3$, then the least value of $\left|z+\frac{1}{4}\right|$ is

If \( |z| \geq 3 \), then the least value of \( |z + 4| \) is

If the complex number \( z \) lies on a circle with center at the origin and radius \( \frac{1}{4} \), then the complex number \( 1 + z \) lies on a circle with radius

If the area of the triangle on the complex plane formed by the points \( z = x + iy \) and \( z = 1 \) is 200, then the value of \( 3 \times |z| \) must be equal to?

If \( \cos \alpha + i \sin \alpha = b \), \( c = \cos \gamma + i \sin \gamma \) and \( b + c + a = 1 \), then \( \cos (\beta - \gamma) + \cos (\alpha - \beta) \) is equal to?

The greatest and the least value of \( z = x + iy \), where \( |z| = 1 \) and \( |x| \leq 3 \), are?

A complex number \( z \) is such that \( \arg \left( \frac{-2}{3} + \frac{2i}{3} \right) = \frac{\pi}{3} \). The points representing this complex number will lie on

If the complex numbers \( z_1, z_2, z_3 \) are in AP, then they lie on a:

If \( x + y = (1 + i \sqrt{3})^{100} \), then find \( (x, y) \):

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

If \(z\) satisfies the equation \(|z|=z-1+2i\), then \(z\) is equal to

If $z$ satisfies the equation $|z|-z=1+2 i$, then $z$ is equal to