Find-the-nth-root-of-1-Find-these-values-when-n-6-

Question Number 155899 by Tawa11 last updated on 05/Oct/21

Find the nth root of 1 . Find these values when n = 6 .

Answered by Ar Brandon last updated on 05/Oct/21

1 = e^{2 k π i}, k \in Z

z_{n} = \sqrt[n]{1} = e^{\frac{2 k π}{n} i}, k \in [0, n - 1]

z_{6} = e^{\frac{k π}{3} i}, k \in [0, 5]

z_{6} = 1, \frac{1}{2} (1 + i \sqrt{3}), - \frac{1}{2} (1 - i \sqrt{3})

- 1, - \frac{1}{2} (1 + i \sqrt{3}), \frac{1}{2} (1 - i \sqrt{3})