Delhi University MCA Complex Numbers Previous Year Questions (PYQs)

Let $z=\cos\!\left(\frac{2\pi}{7}\right)+i\sin\!\left(\frac{2\pi}{7}\right)$. Then the principal argument of $\overline{(1-z^{2}})$ is equal to

The complex number  is the root of the quadratic equation with real coefficients

Let $Re(z)$ and $Im(z)$ be the real and imaginary parts of any complex number $z$, and $\arg(z)$ denotes the principal argument of $z$. Let $z_1$ and $z_2$ be two distinct complex numbers such that $\operatorname{Re}(z_1) = |z_1 - 2| \quad \text{and} \quad \operatorname{Re}(z_2) = |z_2 - 2|.$ If $\arg(z_1 - z_2) = \frac{\pi}{6},$ then