1.NounAn element of a given field (especially, a complex number) x such that for some positive integer n, x = 1."In the case of the field of complex numbers, it follows from de Moivre's formula that the
n
{\displaystyle n}
n
{\displaystyle n}
th roots of unity are
cos
(
k
2
π
n
)
+
i
sin
(
k
2
π
n
)
{\displaystyle \textstyle \cos \left(k{\frac {2\pi }{n}}\right)+i\sin \left(k{\frac {2\pi }{n}}\right)}
, where
k
=
1
,
…
,
n
{\displaystyle k=1,\dots ,n}
."