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Miracle of Euler

The miracle of Euler is the principle value of i raised to the power of i

i i = e− π / 2   or approximately   0.207879576…



From the definition of the logarithm follows that you can write any number as an exponential function, so that

where k ∈ ℤ, the set of integers.

The principle value (for k = 0) is e− π / 2 or approximately 0.207879576...



The Swiss mathematician Leonhard Euler described this calculation in 1748.

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