eenheidswortel

Eenheidswortel is a Dutch term that translates to "root of unity" in English. In mathematics, a root of unity is a complex number that, when raised to a positive integer power, equals 1. Specifically, an n-th root of unity is a solution to the equation z^n = 1, where n is a positive integer.

The roots of unity are fundamental in various areas of mathematics, including abstract algebra, number theory, and signal processing. Geometrically, the n-th roots of unity in the complex plane form the vertices of a regular n-gon inscribed in the unit circle, with one vertex always at the point (1, 0).

The principal n-th root of unity is usually denoted by e^(2πi/n) or exp(2πi/n), where 'i' is the imaginary unit and 'e' is the base of the natural logarithm. All other n-th roots of unity can be obtained by raising this principal root to integer powers from 0 to n-1. For example, the cube roots of unity (n=3) are 1, e^(2πi/3), and e^(4πi/3). These numbers play a significant role in understanding cyclic groups and Fourier analysis.