A (real or complex) scalar u is said to be an nth rootof unity if un = 1. Show that if j and k are positive integers and if uj = ωj−1 n and zk = ω −(k−1) n , then uj, zk, and ujzk are all nth roots of unity.
A (real or complex) scalar u is said to be an nth rootof unity if un = 1. Show that if j and k are positive integers and if uj = ωj−1 n and zk = ω −(k−1) n , then uj, zk, and ujzk are all nth roots of unity.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section: Chapter Questions
Problem 22RE
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Question
A (real or complex) scalar u is said to be an nth root
of unity if un = 1. Show that if j and k are positive integers and if
uj = ωj−1
n and zk = ω
−(k−1)
n , then uj, zk, and ujzk
are all nth roots of unity.
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