Cube roots of Unity and their Properties | #cuberoot | #theoryofquadraticequation |

* mathematics
* algebra
* complex numbers
* number theory
* roots of unity
* cube root of unity
* omega (ω)
* properties of cube roots
* sum of cube roots
* product of cube roots
* geometric interpretation
* applications
* Euler's formula
* De Moivre's theore
* nth roots of unity
* primitive roots of unity
* cyclotomic polynomials
* complex analysis
* discrete mathematics

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* Cube roots of unity are the three complex solutions to the equation x^3 = 1. These roots are 1, ω, and ω², where ω = e^(2πi/3) and ω² = e^(4πi/3). The properties of cube roots of unity include:

1. The sum of the cube roots of unity is zero: 1 + ω + ω² = 0.
2. The product of the cube roots of unity is 1: 1 * ω * ω² = 1.
3. The cube roots of unity are evenly spaced around the unit circle in the complex plane, forming the vertices of an equilateral triangle.

Understanding these properties is essential for solving problems involving polynomial equations and complex numbers.

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