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**Unformatted text preview: **primitive n th root of unity .) (iii) Why do we stop the index at k = n-1? What is z n , z n +1 ? (iv) Plot these n solutions z , z 1 ,...,z n-1 in the the complex plane for (i) n = 2; (ii) n = 3; (iii) n = 4; (iv) for a general n . (Use the one separate plane for each n ). b) Let w = e 2 i/n be the primitive n th root of unity. Consider the matrix U = 1 n [ w jk ] j,k =0 , 1 ,...,n-1 which is, in fact, the Fourier Matrix: U = 1 n 1 1 1 1 1 w w 2 w n-1 1 w 2 w 4 w 2( n-1) . . . . . . . . . . . . 1 w n-1 w 2( n-1) w ( n-1) 2 TRUE or FALSE: U is unitary. Justify your answer. 1...

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