Abstract Algebra: Theory and Applications · Problem 17.6.3

Integral Domains — Thomas Judson

Mathematics — Abstract Algebra · cube-roots-of-unity

Problem

Prove that the cube roots of 1 are given by ω=−1+i32,ω2=−1−i32,ω3=1.\omega = \frac{-1 + i\sqrt{3}}{2}, \quad \omega^2 = \frac{-1 - i\sqrt{3}}{2}, \quad \omega^3 = 1.

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