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de Moivre's Identity

\end{displaymath} (1)

From the Euler Formula it follows that
\end{displaymath} (2)

A similar identity holds for the Hyperbolic Functions,
(\cosh z+\sinh z)^n=\cosh(nz)+\sinh(nz).
\end{displaymath} (3)


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.

© 1996-9 Eric W. Weisstein