List of top Mathematics Questions on Complex numbers asked in MET

If complex number \(z\) lies in the interior or on the boundary of circle of radius 3 units, then maximum and minimum values of \(|z + 1|\) are:

If \( \left| z + \frac{2}{z} \right| = 2 \), then the minimum value of \( |z| \) is

The complex number \(z\) which satisfy the equation \(\left|\frac{1+z}{1-z}\right| = 1\) lies on

If \(\omega\) is a cube root of unity, then \((1 + \omega - \omega^2)(1 - \omega + \omega^2)\) is

If \(1, \omega\) and \(\omega^2\) are the cube roots of unity, then the value of \((1-\omega+\omega^2)(1+\omega-\omega^2)\) is equal to

If \(z = i\log(2 - \sqrt{3})\), then the value of \(\cos z\) will be:

If \(z_1 = 1 + i,\; z_2 = -2 + 3i,\; z_3 = \frac{ai}{3}\) are collinear, where \(i^2 = -1\), then value of \(a\) is:

If \(z_1, z_2\) and \(z_3\) are complex number such that \(|z_1| = |z_2| = |z_3| = \left|\frac{1}{z_1} + \frac{1}{z_2} + \frac{1}{z_3}\right| = 1\) then \(|z_1 + z_2 + z_3|\) is

The locus of the point \(z\) satisfying \(\arg\left(\frac{z-1}{z+1}\right) = k\) (where \(k\) is non-zero) is

Let \(z_1, z_2, z_3\) be three vertices of an equilateral triangle circumscribing the circle \(|z| = 1/2\). If \(z_1 = 1/2 + i\sqrt{3}/2\) and \(z_1, z_2, z_3\) were in anticlockwise sense, then \(z_2\) is

If \(z = \frac{-2}{1 + \sqrt{3}i}\) then the value of \(\arg(z)\) is

Let \(\omega\) is an imaginary cube root of unity, then the value of \(2(1+\omega)(1+\omega^2) + 3(2\omega+1)(2\omega^2+1) + \cdots + (n+1)(n\omega+1)(n\omega^2+1)\) is

If \(z = x + iy\), \(z^{1/3} = a - ib\) then \(\frac{x}{a} - \frac{y}{b} = k(a^2 - b^2)\), where \(k\) is equal to

If $\omega$ is a cube root of unity, then $(1 + \omega - \omega^{2})(1 - \omega + \omega^{2})$ is

The complex numbers $z$ satisfying $\left|\dfrac{i+z}{i-z}\right| = 1$ lie on

If $(\sqrt{3} - i)^{50} = 2^{48}(x - iy)$, then $x^{2} + y^{2}$ equals

Area of the triangle in the Argand diagram formed by the complex numbers $z$, $iz$, $z + iz$ where $z = x + iy$ is

If $\omega$ is an imaginary cube root of 1, then $(1+\omega-\omega^2)^5 + (1-\omega+\omega^2)^5$ is equal to

If $n₁, n₂$ are positive integers, then $(1+i)ⁿ₁+(1+i³)ⁿ₁+(1+i⁵)ⁿ₂+(1+i⁷)ⁿ₂$ is a real number if and only if

The equation $|z+i|-|z-i|=k$ represents a hyperbola, if

If \( n \) is an integer which leaves remainder one when divided by three, then \( (1+\sqrt{3}i)^{n} + (1-\sqrt{3}i)^{n} \) equals

The locus of z satisfying the inequality \( \left| \frac{z+2i}{2z+i} \right| < 1 \), where \( z = x + iy \), is

The value of \( \frac{i^{592} + i^{590} + i^{588} + i^{586} + i^{584}}{i^{582} + i^{580} + i^{578} + i^{576} + i^{574}} \) is:

The value of \( (1 + i)^{4} + (1 - i)^{4} \) is: