Euler's Identity is a famous equation in mathematics that combines five fundamental constants: e , i , \pi , 1, and 0. It is expressed as e^i\pi + 1 = 0 . Here, e is the base of natural logarithms, i is the imaginary unit, and \pi is the ratio of a circle's circumference to its diameter. This identity is celebrated for its beauty and simplicity, linking different areas of mathematics. The identity arises from Euler's formula, which states that e^ix = \cos(x) + i\sin(x) . When x is set to \pi , it leads to the identity. Euler's Identity is often regarded as a profound connection between algebra, trigonometry, and calculus, showcasing the unity of various mathematical concepts.