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In mathematics, de Moivre's formula (also known as de Moivre's theorem and de Moivre's identity) states that for any real number x and integer n it holds that ( + ) = + , where i is the imaginary unit (i 2 = −1).
Feb 13, 2024 · An exploration of the life and times of Abraham De Moivre, his famous theorem, and how it set the stage for the discovery of the Central Limit Theorem.
- Sachin Date
Abraham de Moivre FRS (French pronunciation: [abʁaam də mwavʁ]; 26 May 1667 – 27 November 1754) was a French mathematician known for de Moivre's formula, a formula that links complex numbers and trigonometry, and for his work on the normal distribution and probability theory.
This theorem helps us find the power and roots of complex numbers easily. This pattern was first observed by the French mathematician Abraham De Moivre (1667 – 1754) and was used to find the powers, roots, and even solve equations involving complex numbers.
De Moivre's Theorem is mainly used for computing powers of complex numbers. Understand De Moivre's Theorem, Proof, and Uses along with solved examples and more.
- 13 min
- De Moivre’s formula is given by (cos x + i sin x) n = cos(nx) + i sin(nx)
- De Moivre’s theorem is used to find the roots of complex numbers. It is also used to solve complex numbers raised to powers.
- De Moivre’s formula does not work for non-integer powers.
- The French mathematician Abraham De Moivre invented De Moivre’s theorem.
In probability theory, the de Moivre–Laplace theorem, which is a special case of the central limit theorem, states that the normal distribution may be used as an approximation to the binomial distribution under certain conditions.
In mathematics, the De Moivre’s formula (also known as De Moivre’s theorem) states that for any real number “x” and integer “n,” it holds that, where “i” is the imaginary unit, (i2 = −1).
