Theorems in complex analysis | Articles containing proofs
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).
De Moivre's formula: a COOL proof
A quick way of proving De Moivre's formula! Free ebook http://bookboon.com/en/introduction-to-complex-numbers-ebook Hi again everyone, Chris Tisdell here again. In this presentation I am going to continue my series of videos on complex numbers. In particular, in this presentation, I am g
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Trig identities: De Moivre's formula
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From playlist Intro to Complex Numbers
Using de Moivre's Theorem - example question (1 of 2: Purely real)
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This video explains how to use De Moivre's Theorem to raise complex numbers in trigonometric form to any power. http://mathispower4u.wordpress.com/
From playlist Complex Numbers
Using de Moivre's Theorem - example question (2 of 2: Purely imaginary)
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Complex Polynomial Identity Question (3 of 4: de Moivre's Theorem)
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Visit http://ilectureonline.com for more math and science lectures! In this video I will explain de Moivre's theorem. Next video in the series can be seen at: https://youtu.be/fOzsXySLWlE
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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
From playlist Intro to Complex Numbers
What are complex numbers? | Essence of complex analysis #2
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Some of the links below are affiliate links. As an Amazon Associate I earn from qualifying purchases. If you purchase through these links, it won't cost you any additional cash, but it will help to support my channel. Thank you! Complex Analysis Textbook https://amzn.to/2u5fgl4 (affiliate
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