Euler formula and Euler identity
Fórmula de Euler e identidad de Euler
- Date
- 1748 · confidence high
- Place
- Berlin, Prussia
- Credited to
- Leonhard Euler (Introductio in analysin infinitorum); earlier work by Cotes (1714)
- People
- 👤 Leonhard Euler1707–1783
- Field
- Knowledge & symbols
What was discovered
The equation e^(ix) = cos x + i sin x, whose case x = pi gives e^(i pi) + 1 = 0, unites five fundamental constants. It turns trigonometry into the algebra of complex exponentials.
The 1748 Introductio also establishes the concept of function as the central object of analysis.
What it led to
- complex analysis
- Fourier analysis
- phasors in electrical engineering
- quantum mechanics