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Question Number 14156 by chux last updated on 28/May/17

$$\mathrm{please}\mathrm{what}\mathrm{does}\omega \mathrm{mean}?$$

Answered by RasheedSindhi last updated on 29/May/17

$$\omega \mathrm{is}\mathrm{one}\mathrm{of}\mathrm{the}\mathrm{complex}\mathrm{cube}$$$$\mathrm{roots}\mathrm{of}\mathrm{unity}\left(1\right).$$$$\mathrm{Let}\mathrm{x}\mathrm{is}\mathrm{a}\mathrm{cube}\mathrm{root}\mathrm{of}1$$$$\therefore {\mathrm{x}}^3=1$$$${\mathrm{x}}^3-1=0$$$$(\mathrm{x}-1)({\mathrm{x}}^2+\mathrm{x}+1)=0$$$$\mathrm{x}=1\mid \mathrm{x}=\frac{-1\pm \sqrt{3}\mathrm{i}}{2}$$$$\mathrm{Any}\mathrm{one}\mathrm{of}\mathrm{the}\mathrm{two}\frac{-1\pm \sqrt{3}\mathrm{i}}{2}\mathrm{is}$$$$\mathrm{is}\mathrm{denoted}\mathrm{by}\omega .$$

Commented by chux last updated on 29/May/17

$$\mathrm{wow}....\mathrm{thank}\mathrm{you}\mathrm{sir}.$$

Commented by chux last updated on 29/May/17

$$\mathrm{how}\mathrm{is}\mathrm{it}\mathrm{related}\mathrm{to}$$$$\cos \left(2\pi /3\right)+\mathrm{isin}\left(2\pi /3\right)....$$$$$$$$\mathrm{Thanks}\mathrm{in}\mathrm{advance}.$$

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