Roots of unity 🥕

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The $n$-th roots of unity are the complex numbers $z$ that satisfy the equation:

$$z^n =1\quad \text{or equivalently}\quad z^n -1 = 0$$

using Euler’s formula, we can find all $n$ distinct roots. They are given by:

$$z_k=e^{i\dfrac{2\pi k}{n}}=\cos\left(\dfrac{2\pi k}{n}\right) + i\sin\left(\dfrac{2\pi k}{n}\right), \quad k=0, 1, 2,\cdots,n-1.$$

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