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Question Number 216487 by Tawa11 last updated on 08/Feb/25

$$\mathrm{Find}\mathrm{the}\mathrm{value}\mathrm{of}{\omega }^7+{\omega }^8+{\omega }^{12}\mathrm{where}$$$$\omega \mathrm{is}\mathrm{omega}\mathrm{function}.$$

Commented by mr W last updated on 09/Feb/25

$$canyouspecifywhatyouromega$$$$function\omega means?$$

Commented by Tawa11 last updated on 09/Feb/25

$$\mathrm{Ohh}.$$$$\mathrm{It}\mathrm{will}\mathrm{be}\mathrm{cube}\mathrm{root}\mathrm{of}\mathrm{unity}\mathrm{sir}.$$$$\mathrm{Sorry}\mathrm{for}\mathrm{not}\mathrm{specifying}.$$

Answered by Rasheed.Sindhi last updated on 09/Feb/25

$$\begin{array}{c}{\omega }^3=1\\ {\omega }^2+\omega +1=0\end{array}\}$$$$={\left({\omega }^3\right)}^2.\omega +{\left({\omega }^3\right)}^2.{\omega }^2+{\left({\omega }^3\right)}^4$$$$=\omega +{\omega }^2+1$$$$=0$$

Commented by Tawa11 last updated on 09/Feb/25

$$\mathrm{Thanks}\mathrm{sir}.$$

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