Search results
Results from the WOW.Com Content Network
A modest extension of the version of de Moivre's formula given in this article can be used to find the n-th roots of a complex number for a non-zero integer n. (This is equivalent to raising to a power of 1 / n). If z is a complex number, written in polar form as = ( + ),
The theorem appeared in the second edition of The Doctrine of Chances by Abraham de Moivre, published in 1738. Although de Moivre did not use the term "Bernoulli trials", he wrote about the probability distribution of the number of times "heads" appears when a coin is tossed 3600 times.
Therefore, given a power z a of z, one has z a = z r, where 0 ≤ r < n is the remainder of the Euclidean division of a by n. Let z be a primitive n th root of unity. Then the powers z, z 2, ..., z n−1, z n = z 0 = 1 are n th roots of unity and are all distinct. (If z a = z b where 1 ≤ a < b ≤ n, then z b−a = 1, which would imply that z ...
Published in 1738 by Woodfall and running for 258 pages, the second edition of de Moivre's book introduced the concept of normal distributions as approximations to binomial distributions. In effect de Moivre proved a special case of the central limit theorem. Sometimes his result is called the theorem of de Moivre–Laplace.
Theorem of de Moivre–Laplace, a central limit theorem Topics referred to by the same term This disambiguation page lists articles associated with the title De Moivre's theorem .
Maximum power theorem (electrical circuits) Maxwell's theorem (probability theory) May's theorem (game theory) Mazur–Ulam theorem (normed spaces) Mazur's torsion theorem (algebraic geometry) Mean value theorem ; Measurable Riemann mapping theorem (conformal mapping) Mellin inversion theorem (complex analysis) Menelaus's theorem
Language links are at the top of the page. Search. Search
That cos nx is an n th-degree polynomial in cos x can be seen by observing that cos nx is the real part of one side of de Moivre's formula: + = ( + ). The real part of the other side is a polynomial in cos x and sin x , in which all powers of sin x are even and thus replaceable through the identity cos 2 x + sin 2 x = 1 .