 |
(1)
|
From the Euler formula it follows that
 |
(2)
|
A similar identity holds for the hyperbolic functions,
 |
(3)
|
de Moivre's Identity
See also
Euler FormulaExplore with Wolfram|Alpha
References
Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 356-357, 1985.Courant, R. and Robbins, H. What Is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed. Oxford, England: Oxford University Press, pp. 96-100, 1996.Nagell, T. Introduction to Number Theory. New York: Wiley, p. 156, 1951.Referenced on Wolfram|Alpha
de Moivre's IdentityCite this as:
Weisstein, Eric W. "de Moivre's Identity." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/deMoivresIdentity.html