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Euler's identity, a special case of Euler's formula, is the following:
The equation appears in Leonhard Euler's Introductio, published in Lausanne in 1748. In this equation, e is the base of the natural logarithm, <math>i</math> is the imaginary unit (an imaginary number with the property i² = 1), and <math>\pi</math> is Archimedes' constant pi (π, the ratio of the circumference of a circle to its diameter).
It was called "the most remarkable formula in mathematics" by Richard Feynman. Feynman found this formula remarkable because it links some very fundamental mathematical constants:
The formula also involves the fundamental arithmetical operations of addition, multiplication and exponentiation.
The formula is a special case of Euler's formula from complex analysis, which states that
for any real number <math>x</math>. If we set <math>x = \pi</math>, then
and since cos(π) = 1 and sin(π) = 0, we get
and
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