< **1** 2 >

### Algebraic number

An algebraic number is a root of an equation in the form

in which the coefficients *a*_{0}, *a*_{1}, ... *a _{n}* are all integers.

##### Examples

1. All rational numbers are algebraic because the fraction *a / b* is a solution of *bx – a = *0.

2. The irrational number √2 is algebraic because it is a solution of *x*^{2} − 2 = 0.

3. The imaginary unit *i* is algebraic, as it is a root of *x*^{ 2} + 1 = 0.

##### Additional information

If a real number or a complex number is not algebraic, it is called a transcendental number.

The algebraic numbers are countable as the number of polynomials with integer coefficients (and the number of roots per polynomial) are countable.