ühikjuured

ühikjuured refers to the roots of unity in mathematics. These are complex numbers that, when raised to a positive integer power, equal 1. Specifically, the n-th roots of unity are the solutions to the equation z^n = 1, where n is a positive integer.

Geometrically, the n-th roots of unity can be visualized as points on the unit circle in the complex plane. They form the vertices of a regular n-sided polygon inscribed in the unit circle, with one vertex always at the point (1, 0).

The n-th roots of unity can be expressed using Euler's formula. For a positive integer n, the n distinct n-th roots of unity are given by e^(2πik/n) for k = 0, 1, 2, ..., n-1. This can also be written in trigonometric form as cos(2πk/n) + i sin(2πk/n).

The most basic root of unity is 1, which is the first root of unity. The square roots of unity are 1 and -1. The cube roots of unity are 1, e^(2πi/3), and e^(4πi/3). These concepts are fundamental in various areas of mathematics, including abstract algebra, number theory, and signal processing. They play a role in the study of cyclic groups and are important in the development of algorithms like the Fast Fourier Transform.