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is a discrete version of the orthogonality relationship in Exercise 4(a) above. To see this, fix N ∈ Z and, for each k ∈ Z, put zk = e2πik/N . Now do the following:
(a) Show that z = zk is a solution to the equation zN − 1 = 0. (The N distinct complex numbers z0,…,zN−1 are known as the Nth roots of unity.)
(b) Plot zk for k = 0,…, N − 1 for several values of N, say N = 2, 3, 4, and 8
(c) Argue that 0.