Complex number that is not algebraic.

A transcendental number is a real or complex irrational number that cannot be expressed as the root of a polynomial equation.

### Examples

- The numbers π and
*e*are real irrational transcendental numbers. - The number \(2^{\sqrt{2}}\) is also a real transcendental number.
- The number \(\sqrt{5}\) is an irrational number, but it is not transcendental, because it is the solution to the equation
*x*² – 5 = 0. - The number \(e^{i}\) is a complex transcendental number.