# Transcendental Number

## Transcendental Number

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 x² – 5 = 0.
• The number $$e^{i}$$ is a complex transcendental number.