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. It is a special case of Euler's formula e i x = cos ⁡ x + i sin ⁡ x {\displaystyle e^{ix}=\cos x+i\sin x} when evaluated for x = π {\displaystyle x=\pi } . Euler's identity is considered an exemplar of mathematical beauty, as it shows a profound connection between the most fundamental numbers in mathematics.