Euler's Identity: The Gold Standard of Mathematics

Euler's Identity

"The most remarkable formula in mathematics" - Richard Feynman

The general identity can be proved using the infinite series of e, sin x, cos x. 

(Where i is the imaginary unit of complex numbers)

Substituting pi for x and re-arranging gives:

The three basic arithmetic operations occur exactly once each: addition, multiplication, and exponentiation.

The identity also links five fundamental mathematical constants:

• e: the base of natural logarithms
• i: the imaginary unit of complex numbers  
• π: the ratio of the circumference of a circle to its diametre
•  1: the multiplicative identity
• 0: the additive identity

  
QED