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.