Question and Answers Forum

All Questions      Topic List

Number Theory Questions

Previous in All Question      Next in All Question      

Previous in Number Theory      Next in Number Theory      

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

Prove that the product for all  nth roots of unity is equal to zero,  except n=1.     Note:  U_n ={e^(2kπi/n)  ∣ k∈{1, 2, ..., n}}  x^n =1

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{product}\:\mathrm{for}\:\mathrm{all} \\ $$$${n}\mathrm{th}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{unity}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{zero}, \\ $$$$\mathrm{except}\:{n}=\mathrm{1}. \\ $$$$\: \\ $$$$\mathrm{Note}: \\ $$$${U}_{{n}} =\left\{{e}^{\mathrm{2}{k}\pi{i}/{n}} \:\mid\:{k}\in\left\{\mathrm{1},\:\mathrm{2},\:...,\:{n}\right\}\right\} \\ $$$${x}^{{n}} =\mathrm{1} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com