De Moivres theorem Notes

Abraham De Moivre (1667-1754) was born in France, but fled to England in 1688, after being imprisoned for his religious beliefs. A brilliant mathematician, he was unable to gain a university appointment (because he was born in France) or escape his life of poverty, gaining only a meagre income as a private tutor. He was friends with Sir Isaac Newton and Edmund Halley (1656 - 1742), was elected to the Royal Society in England, and to the Academies of Paris and Berlin, yet in spite of the support of the great Leibniz (1646 - 1716), and of Jacques Bernoulli, he never gained a university appointment and died in relative poverty. In spite of this, he made many discoveries in mathematics, some of which are attributed to others This page deals with the proof of De Moivre's Theorem, etc. It has formula to compute the cosine and sine directly, but these require further algebraic manipulation, to reduce the sines in the cosine formula, and the cosines in the sine formula. This work is extended later beginning with the cosine , where formulae are also derived to calculate directly the coefficients of a given power in a given expansion for cos nx and sin nx. Before that, some pages, mentioned below, deal with the Chebyshev method.

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