Euler's identity

: I hate math , but while doing this series I began to love it...:



In mathematical analysis, Euler's identity, named after Leonhard Euler, is the equation

e^{i \pi} =-1

where

e -[link] is Euler's number, the base of the natural logarithm,
i-[link] is the imaginary unit, one of the two complex numbers whose square is negative one (the other is -i\,\!), and
pi-[link] is pi, the ratio of the circumference of a circle to its diameter.

Euler's identity is considered by many to be remarkable for its mathematical beauty. Three basic arithmetic operations occur exactly once each: addition, multiplication, and exponentiation. The identity also links five fundamental mathematical constants:

* The number 0.
* The number 1.
* The number π, which is ubiquitous in trigonometry, geometry of Euclidean space, and mathematical analysis (π ≈ 3.14159).
* The number e, the base of natural logarithms, which also occurs widely in mathematical analysis (e ≈ 2.71828).
* The number i, imaginary unit of the complex numbers, which contain the roots of all nonconstant polynomials and lead to deeper insight into many operators, such as integration.


credits:~insurrectionx