Solved: A (real or complex) scalar u is said to be an nth root of unity if un = 1. (a)
Chapter 5, Problem 36(choose chapter or problem)
A (real or complex) scalar u is said to be an nth root of unity if un = 1. (a) Show that if u is an nth root of unity and u = 1, then 1 + u + +u2 ++ un1 = 0 [Hint: 1un = (1u)(1+u+u2 ++un1)] (b) Let n = e 2i n . Use Eulers formula (ei = cos + isin ) to show that n is an nth root of unity. (c) Show that if j and k are positive integers and if uj = j1 n and zk = (k1) n , then uj, zk, and ujzk are all nth roots of unity.
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