Algebraic Number/Examples

Examples of Algebraic Numbers
The algebraic numbers include:
 * The elements of the set of rational numbers $\Q$, since these are roots of linear polynomials -- see Rational Number is Algebraic
 * $\sqrt 2$, since it is a root of $x^2 - 2$
 * $\sqrt [3] {2 + \sqrt 2}$, since it is a root of $x^6 - 4 x^3 + 2$
 * $\sqrt 3 + \sqrt 2$, since it is a root of $x^4 - 10 x^2 + 1$
 * $\sqrt [3] 4 - 2 i$, since it is a root of $x^6 + 12 x^4 - 8 x^3 + 48 x^2 + 96 x + 80$
 * The golden section $\varphi$, since it is a root of $x^2 - x - 1$
 * The imaginary unit $i$, since it is a root of $x^2 + 1$