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de Moivre Number

A solution zeta_k=e^(2piik/d) to the cyclotomic equation

x^d=1.

The de Moivre numbers give the coordinates in the complex plane of the polygon vertices of a regular polygon with d sides and unit radius.

dde Moivre number
2+/-1
31, 1/2(-1+/-isqrt(3))
4+/-1,+/-i
51, 1/4(-1+sqrt(5)+/-isqrt(10+2sqrt(5))), 1/4(-1-sqrt(5)+/-isqrt(10-2sqrt(5)))
6+/-1,+/-1/2(+/-1+isqrt(3))

See also

Cyclotomic Equation, Cyclotomic Polynomial, Euclidean Number

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References

Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, 1996.

Referenced on Wolfram|Alpha

de Moivre Number

Cite this as:

Weisstein, Eric W. "de Moivre Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/deMoivreNumber.html

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