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Question Number 197299 by bbbbbbbb last updated on 12/Sep/23

$$\sqrt[6]{-64}-\sqrt[10]{-10}=?$$$$\mathit{I}\mathbf{need}\mathbf{so}\mathbf{much}\mathbf{plz}$$

Answered by Frix last updated on 13/Sep/23

$$\mathrm{\forall }n\in \mathbb{N}\mathrm{\setminus }\left\{0\right\}:-n=n{\mathrm{e}}^{\mathrm{i}\pi }\Rightarrow$$$$\sqrt[k]{-n}=\sqrt[k]{n}{\mathrm{e}}^{\mathrm{i}\frac{\pi }{k}}=\sqrt[k]{n}(\cos \frac{\pi }{k}+\mathrm{i}\sin \frac{\pi }{k})$$

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