If $2 \cos \frac{7 \pi}{5}$ is one of the values of $z^{\frac{1}{5}}$,then $z=$

The number of real values of $(-1-\sqrt{3} i)^{3/4}$ is

If $\alpha, \beta$ are the roots of the equation $x^2+x+1=0$,then $(\alpha+\beta)^2+(\alpha^2+\beta^2)^2+(\alpha^3+\beta^3)^2+\ldots+(\alpha^{12}+\beta^{12})^2=$

Let $a = \cos 1^{\circ}$ and $b = \sin 1^{\circ}$. We say that a real number is algebraic if it is a root of a polynomial with integer coefficients. Then,

If $\omega$ is a complex root of the equation $z^3 = 1$,then $\omega + \omega^{\left( \frac{1}{2} + \frac{3}{8} + \frac{9}{32} + \frac{27}{128} + \dots \right)}$ is equal to

If $Z \neq 0$ is a complex number such that $Z^2 + Z|Z| + |Z|^2 = 0$,then $Z$ is in the set (Here $\omega$ is a complex cube root of unity).