The cube roots of unity are the three complex numbers that satisfy the equation z^3 = 1, where z is a complex number. These solutions can be found by using the formula:
z = e^(2πik/3)
where k = 0, 1, or 2.
Therefore, the three cube roots of unity are:
ω1 = e^(2πi/3) = (-1 + sqrt(3)i)/2
ω2 = e^(4πi/3) = (-1 - sqrt(3)i)/2
ω3 = e^(2πi) = 1
Note that ω1 and ω2 are complex conjugates of each other, and they are also called primitive cube roots of unity.
The cube roots of unity are the complex solutions to the equation z^3 = 1. These solutions are given by:
1, (-1 + sqrt(3)i)/2, and (-1 - sqrt(3)i)/2
where i is the imaginary unit, which is defined as the square root of -1.
So these three values are the cube roots of unity.
1+w+w2 =0
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