Euler's formula is a mathematical formula that is used in complex analysis. It shows a relationship between the trigonometric functions and the complex exponential functions. It was named after Leonhard Euler. Mathematically this formula is shown as:

e

^{ix}= because x + I sin x

This formula was proved by Roger Cotes in the year 1714, whereas Euler further refined it in its current form in the year 1748. He also published it and based his proof on the Infinite series of both sides that are equal.