(1667-1754) French mathematician who pioneered the development of analytical trigonometry, for which he formulated his theorem regarding complex numbers. He also devised a means of research into the theory of probability.
De Moivre was born in Vitry-le-François, Champagne, and studied in Paris. With the revocation of the Edict of Nantes 1685, he was imprisoned as a Protestant for 12 months; on his release he went immediately to England. In London he became a close friend of Isaac Newton and Edmund Halley, but he never obtained a permanent position; he eked out a precarious living by tutoring and acting as a consultant for gambling syndicates and insurance companies.
His The Doctrine of Chances was published first in Latin and then in expanded English versions 1718, 1738, and 1758. It was one of the first books on probability, and made an approximation to the normal or Gaussian distribution, which was incorporated into statistical studies for the next 200 years. De Moivre was the first to derive an exact formulation of how “chances” and stable frequency are related.
Analyzing mortality statistics, De Moivre laid the mathematical foundations of the theory of annuities, for which he devised formulae based on a postulated law of mortality and constant rates of interest on money. First published 1725, his work became standard in textbooks of all subsequent commercial applications.
In analytical trigonometry he discovered an equation that is now named for him:
(cos z + i sin z)n = cos nz + i sin nz
First stated 1722, it had been anticipated by related forms 1707. It became one of the most useful steps in the early development of complex number theory.