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 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.