Consider the algebriac number $\displaystyle \alpha$ with the minimum polynomial $\displaystyle m_{\alpha}{Q} = x^3 + x + 1 $

-How many numbers in C(complex numbers) have $\displaystyle m_{\alpha}{Q}$ as its minimum polynomial? List the complex numbers.

-Simplify $\displaystyle 1 + 2\alpha + 3\alpha^{3}$ into reduced form.