Euler's formula, named after Leonhard Euler, is a mathematical formula in that shows a deep relationship between the trigonometric functions and the complex exponential function. Euler's formula states that, for any real number x,
The formula is still valid if x is a complex number.
Richard Feynman called Euler's formula "our jewel"[Feynman, Richard P. (1977). The Feynman Lectures on Physics, vol. I.Addison-Wesley.] and "one of the most remarkable, almost astounding, formulas in all of mathematics".