Euler's identity, also known as Euler's formula, is one of the most fascinating formulas in mathematics, which connects several most important constants in mathematics: two transcendental numbers: the base e and pi of natural logarithm, two units: imaginary number unit I and natural number unit 1, and the common 0 in mathematics.

Euler's identity refers to the following relationship:

E I π+ 1 = 0 where E is the base of natural index, I is imaginary unit and π is π.

This identity first appeared in the book Introduction published by Euler in Lausanne on 1748. This is the characteristic of Euler formula of complex analysis.

Example: for any real number x, e ix = cosx+isinx, substituting x = π gives an identity.

Richard feynman called this identity "the most wonderful formula in mathematics" because it concisely connected five basic mathematical constants.