De Moivre’s theorem

On the other hand, the Taylor expansion of Y gives the coefficient ak with de Moivre s theorem in the form48,49 ... 

Rule 5 must be modified slightly for higher-order systems. See de Moivre s theorem. 

Beginning with de Moivre s theorem, more useful identities involving sines and cosines can be derived. For example, setting n = 2,... 

De Moivre s theorem can be used to determine the nth roots of unity, namely the n complex roots of the equation... 

De Moivre s theorem, Eq. (4.37), remains valid even for noninteger values of n. Replacing n by 1/m, we can write... 

The solution is bifurcated and, for valnes of < 4y, the argument within the square root sign in Equations (12.71) and (12.72) become imaginary and, using De Moivre s theorem and equating the real parts. 

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