Euler's identity
In mathematics, Euler's identity (also known as Euler's equation) is the equality e i π + 1 = 0 {\displaystyle e^{i\pi }+1=0} where e {\displaystyle e} is Euler's number, the base of natural logarithms, i {\displaystyle i} is the imaginary unit, which by definition satisfies i 2 = − 1 {\displaystyle i^{2}=-1} , and π {\displaystyle \pi } is pi, the ratio of the circumference of a circle to its diameter. Euler's identity is named after the Swiss mathematician Leonhard Euler.