“cube root of unity”的概念、定义、翻译、参考文献-科学参考

cube root of unity

Mathematics

单词	cube root of unity
释义	cube root of unity Mathematics A complex number z such that z³ = 1. The three cube roots of unity are 1, ω‎ and ω‎², where $\begin{array}{l} ω & = e^{2 π i / 3} = cos \frac{2 π}{3} + i sin \frac{2 π}{3} \\ = - \frac{1}{2} + \frac{\sqrt{3}}{2} i, \end{array}$ $\begin{array}{l} ω^{2} & = e^{4 π i / 3} = cos \frac{4 π}{3} + i sin \frac{4 π}{3} \\ = - \frac{1}{2} - \frac{\sqrt{3}}{2} i . \end{array}$ Properties: (i) $ω^{2} = \bar{ω}$ (see conjugate), (ii) 1 + ω‎ + ω‎² = 0.
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