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What is De-Moivre`s theorem in complex numbers ?

What is De-Moivre`s theorem in complex numbers ?

Grade:12

1 Answers

bharat bajaj IIT Delhi
askIITians Faculty 122 Points
7 years ago

De Moivre’s Theorem :

It is a formulauseful for findingpowersandrootsofcomplex numbers.

(\cos x + i \sin x)^n = \cos (nx) + i \sin (nx).\,
Say, given a complex number z, and you have to find its cube. Dont use the usual method to multiply z three times. It becomes easier from De moivre's theorem.
z^3 = r^3 ( cosx + sinx)^3 = r^3 ( cos3x + sin3x)
Thanks

Bharat Bajaj
IIT Delhi

askiitians faculty

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