List of top Mathematics Questions on Complex Numbers and Quadratic Equations asked in COMEDK UGET

The polynomial \[ p(x)=x^4-5x^2+4 \] has:
Given that \( z \) is a real number and \( z = \frac{\lambda + 4i}{1+\lambda i} \) where \( \lambda \in R \), then the possible value of \( \lambda \) is:
If \( z = \left(\frac{\sqrt{3}}{2} + \frac{i}{2}\right)^5 + \left(\frac{\sqrt{3}}{2} - \frac{i}{2}\right)^5 \), then
If for real values of \( x \), \( \cos \theta = x + \frac{1}{x} \), then x is
The complex number \( \frac{1 + 7i}{(2 - i)^2 \) lies in}
Amplitude of the complex number $i\, \sin \bigg( \frac{\pi}{19} \bigg)$ is
If $\alpha, \beta , \gamma$ are the roots of the equation $x^3 - 3x^2 + 2x - 1 = 0$ then the value of $[(1 - \alpha) (1 -\beta )(1 - \gamma)]$ is
If $Z$ is a complex number with $I Z I = 1$ and $Z + \frac{1}{Z} = x + iy$, then $xy = $
If $ \sqrt{x} + \frac{1}{\sqrt{x}} = 2 \, \cos \theta $, then $x^6 + x^6 = $