Theorems in complex analysis | Articles containing proofs

De Moivre's formula

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 (i2 = −1). The formula is named after Abraham de Moivre, although he never stated it in his works. The expression cos x + i sin x is sometimes abbreviated to cis x. The formula is important because it connects complex numbers and trigonometry. By expanding the left hand side and then comparing the real and imaginary parts under the assumption that x is real, it is possible to derive useful expressions for cos nx and sin nx in terms of cos x and sin x. As written, the formula is not valid for non-integer powers n. However, there are generalizations of this formula valid for other exponents. These can be used to give explicit expressions for the nth roots of unity, that is, complex numbers z such that zn = 1. (Wikipedia).

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De Moivre's formula: a COOL proof

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Trig identities: De Moivre's formula

How to obtain trig identities from De Moivre's formula. Free ebook http://bookboon.com/en/introduction-to-complex-numbers-ebook Okay so we are asked to write sin4θ in terms of cosθ and sinθ by applying De Moivre’s Theorem, or De Moivre’s formula, and hence write this product as a functio

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Using de Moivre's Theorem - example question (1 of 2: Purely real)

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De Moivre's Theorem

This video explains how to use De Moivre's Theorem to raise complex numbers in trigonometric form to any power. http://mathispower4u.wordpress.com/

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Calculus 2: Complex Numbers & Functions (18 of 28) de Moivre's Theorem

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Investigating de Moivre's Theorem (1 of 3: Why must we be cautious?)

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Application of De Moivre's theorem

How to produce trig identities from De Moivre's theorem. Free ebook http://bookboon.com/en/introduction-to-complex-numbers-ebook You are asked to write cos5θ in terms of cosθ by applying De Moivre’s theorem or De Moivre’s formula. So let us just remind ourselves what that is. For each in

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De Moivre's Theorem

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