Euler's formula (redirected from Complex exponential)

Euler's formula

Either of two important mathematical theorems of Leonhard Euler. The first is a topological invariance (see topology) relating the number of faces, vertices, and edges of any polyhedron. It is written F + V = E + 2, where F is the number of faces, V the number of vertices, and E the number of edges. A cube, for example, has 6 faces, 8 vertices, and 12 edges, and satisfies this formula. The second formula, used in trigonometry, says e^ix = cos x + isin x where e is the base of the natural logarithm and i is the square root of −1 (see irrational number). When x is equal to π or 2π, the formula yields two elegant expressions relating π, e, and i: e^iπ = −1 and e^2iπ = 1.

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Euler's formula [′ȯi·lərz ‚fȯr·myə·lə]

(mathematics)

The formulae^ix= cosx+isinx,wherei= √(-1).