The first five points of the 8-point DFT of a real valued sequence are 5, 1 – j3, 0, 3 – j4 and 3 + j4. The last two points of the DFT are respectively

The correct answer is $\boxed{\text{A. }0, 1 – j3}$.

The 8-point DFT of a real-valued sequence is a complex-valued sequence of length 8. The first four points of the DFT are real, and the last four points are complex conjugates of the first four points.

The first five points of the DFT are given as $5, 1 – j3, 0, 3 – j4, 3 + j4$. The last two points of the DFT are therefore $1 – j3$ and $0$.

Here is a brief explanation of each option:

• Option A: $0, 1 – j3$. This is the correct answer. The first five points of the DFT are given as $5, 1 – j3, 0, 3 – j4, 3 + j4$. The last two points of the DFT are therefore $1 – j3$ and $0$.
• Option B: $0, 1 + j3$. This is not the correct answer. The last two points of the DFT cannot be both real.
• Option C: $1 + j3, 5$. This is not the correct answer. The last two points of the DFT cannot be both complex.
• Option D: $1 – j3, 5$. This is not the correct answer. The last two points of the DFT cannot be both real and complex.