Algebraic Number/Examples/Cube Root of 4 minus 2 i

Example of Algebraic Number

 * $\sqrt [3] 4 - 2 i$ is an algebraic number.

Proof
Let $x = \sqrt [3] 4 - 2 i$.

We have that:

Thus $\sqrt [3] 4 - 2 i$ is a root of $x^6 + 12 x^4 - 8 x^3 + 48 x^2 + 96 x + 80 = 0$.

Hence the result by definition of algebraic number.