de Moivre Number

A solution $\zeta_k=e^{2\pi i k/d}$ to the Cyclotomic Equation

$$x^d=1.$$

The de Moivre numbers give the coordinates in the Complex Plane of the Vertices of a regular Polygon with $d$ sides and unit Radius.

$n$	de Moivre Number
2	$\pm 1$
3	1, ${\textstyle{1\over 2}}(-1\pm i\sqrt{3}\,)$
4	$\pm 1, \pm i$
5	1, ${1\over 4}(-1+\sqrt{5}\pm i\sqrt{10+2\sqrt{5}}\,)$, ${\textstyle{1\over 4}}(-1-\sqrt{5}\pm i\sqrt{10-2\sqrt{5}}\,)$
6	$\pm 1, \pm{\textstyle{1\over 2}}(\pm 1+i\sqrt{3}\,)$

See also Cyclotomic Equation, Cyclotomic Polynomial, Euclidean Number

References

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