Prove-that-the-product-for-all-nth-roots-of-unity-is-equal-to-zero-except-n-1-Note-U-n-e-2kpii-n-k-1-2-n-x-n-1-

Question Number 21756 by FilupS last updated on 03/Oct/17

Prove that the product for all

n th roots of unity is equal to zero,

except n = 1 .

Note :

U_{n} = {e^{2 k π i / n} ∣ k \in {1, 2, \dots, n}}

x^{n} = 1