36. The following 8-point sequences are defined over 0 ? n ? 7. Without computing their DFTs, determine which have real-valued 8-point DFTs and which have 8-point imaginary-valued DFTs. If DFTs are complex valued, explain why.
(a) $x_1[n] = \{0, -3, 1, -2, 0, 2, -1, 3\}$.
(b) $x_2[n] = \{5, 2, -9, 4, 7, 4, -9, 2\}$.
(c) $x_3[n] = \{8, -3, 1, -2, 6, 2, -1, 3\}$.
(d) $x_4[n] = \{0, 1, 3, -2, 5, 2, -3, 1\}$.
(e) $x_5[n] = \{10, 5, -7, -4, 5, -4, -7, 5\}$.