The roots of the equation $x^4 - 1 = 0$ are

If $\omega$ is a complex cube root of unity,then $(x - y)(x\omega - y)(x\omega^2 - y) = $

The product of all the roots of ${\left( \cos \frac{\pi }{3} + i\sin \frac{\pi }{3} \right)^{3/4}}$ is

Let $\omega (\neq 1)$ be a cubic root of unity. Then the minimum value of the set $\{|a+b\omega+c\omega^2|^2 : a, b, c \text{ are distinct non-zero integers}\}$ equals

If $1, \omega, \omega^2$ are the cube roots of unity and $\alpha = \omega + 2\omega^2 - 3$,then $\alpha^3 + 12\alpha^2 + 48\alpha + 3$ equals

If $\alpha, \beta$ are the roots of $x^2-x+1=0$,then the quadratic equation whose roots are $\alpha^{2015}$ and $\beta^{2015}$ is