List of top Mathematics Questions on Complex numbers asked in MHT CET

If \(\alpha\) and \(\beta\) are complex cube roots of unity, then the difference between the values of \(\alpha ^{2}+\beta ^{2}+\alpha \beta\) and \(\alpha ^{4}+\beta ^{4}+\alpha ^{-1}\beta ^{-1}\) is

If \(|z-5i|=|z+3|\), where \(z\) is a complex number, then the equation of the locus of \(z\) in Cartesian coordinates is ...

If \(\omega\) is a complex cube root of unity, then the value of the expression \((1-\omega +\omega ^{2})^{7}+(1+\omega -\omega ^{2})^{7}\) is equal to...

If \(n\in Z\), then the value of \(\frac{2^{n}}{(1+i)^{2n}}+\frac{2^{n}}{(1-i)^{2n}}+\frac{(1+i)^{2n}+(1-i)^{2n}}{2^{n}}\) is equal to

If \(x=\frac{25}{3-4i}\) then \(2x^{3}-11x^{2}+44x+27=\)

If \(z=\frac{\sqrt{3}+i}{2}\), then the value of \(z^{69}\) is

The modulus and argument of \((1+i\sqrt{3})^{8}\) are respectively...

If \(z = \sum _{n = 0}^{2026}i^n\), where \(i = \sqrt{-1}\), then one of the values of \(\sqrt{z}\) is...

\(\frac{(cos2θ+isin2θ)^7}{(cos4θ+isin4θ)^3} =\)

If \(n\) is a positive integer, then \((1+i\sqrt{3})^{2n}+(1-i\sqrt{3})^{2n}\) is equal to .........

If \(ω\) is a complex cube root of unity, then the value of the expression \(2(1+\frac{1}{ω})(1+\frac{1}{ω^2})+3(2+\frac{1}{ω})(2+\frac{1}{ω^2})+\ldots +(n+1)(n+\frac{1}{ω})(n+\frac{1}{ω^2})\) is...

If \(x = \sqrt{-1-\sqrt{-1-\sqrt{-1-\ldots \infty }}}\), where \(ω\) is a non-real complex cube root of unity, then the value of \(x\) is...

The polar form of the complex number \(z = \frac{1}{1+i}\), (where \(i = \sqrt{-1}\)) is

If \(α\) and \(β\) are the roots of the equation \(x^2+x+1 = 0\) then \(α^{2026}+β^{2026} =\)

If \(-1+\sqrt{-3} = re^{iθ}\), then the value of \(θ\) is

The general solution of $x(x - 1)\frac{dy}{dx} = x^3(2x - 1) + (x - 2)y$ is

The projection of the line segment joining the points \( (2, 1, -3) \) and \( (-1, 0, 2) \) on the line whose direction ratios are \( 3, 2, 6 \) is

If two sides of a triangle are \( \sqrt{3} - 1 \) and \( \sqrt{3} + 1 \) units and their included angle is \( 60^\circ \), then the third side of the triangle is

If $y = \log_e x^3 + 3 \sin^{-1} x + kx^2$ and $y'\left(\frac{1}{2}\right) = 2\sqrt{3}$, then $k =$}

The equation $|z + 1 - i| = |z - 1 + i|$ represents a (where z is a complex number)

If two sides of a triangle are \( \sqrt{3} - 1 \) and \( \sqrt{3} + 1 \) units and their included angle is \( 60^\circ \), then the third side of the triangle is

The projection of the line segment joining the points \( (2, 1, -3) \) and \( (-1, 0, 2) \) on the line whose direction ratios are \( 3, 2, 6 \) is

If the amplitude of $(z - 2 - 3i)$ is $\frac{3\pi}{4}$, then the locus of $z$ is (where $z = x + iy$)