1-1-3-1-1-3-

Question Number 189559 by 073 last updated on 18/Mar/23

{(- 1)}^{\frac{1}{3}} = ?

\sqrt[3]{- 1} = ?

Answered by Frix last updated on 18/Mar/23

- 1 = e^{i π}

\Rightarrow

{(- 1)}^{\frac{1}{n}} = e^{i \frac{π}{n}} = \cos \frac{π}{n} + i \sin \frac{π}{n}

{(- 1)}^{\frac{1}{2}} = e^{i \frac{π}{2}} = \cos \frac{π}{2} + i \sin \frac{π}{2} = i

{(- 1)}^{\frac{1}{3}} = \cos \frac{π}{3} + i \sin \frac{π}{3} = \frac{1}{2} + \frac{\sqrt{3}}{2} i

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