A transcendental number is a complex number that is not an algebraic number. That is, it is a complex number that is transcendental over $\mathbb{Q}$ (or, equivalently, over $\mathbb{Z}$).

Well known transcendental numbers include $\pi$ and $e$ (the base of natural logarithms).

Cantor showed that, in a sense, “almost all” complex numbers are transcendental: there are uncountably many complex numbers, but only countably many algebraic numbers.