Consider the sequence x[n] = {-4 – j5, 1 + j2, 4} The conjugate antisymmetric part of the sequence is

The correct answer is A.

The conjugate antisymmetric part of a sequence is defined as follows:

$$x_{an} = \overline{x_{-n}}$$

where $\overline{x}$ denotes the complex conjugate of $x$.

In this case, we have:

$$x[n] = {-4 – j5, 1 + j2, 4}$$

Therefore, the conjugate antisymmetric part of the sequence is:

$$x_{an} = \overline{x_{-n}} = {-4 + j5, 1 – j2, 4}$$

which can be simplified to:

$$x_{an} = {-4 – j2.5, j2, 4 – j2.5}$$

Here is a brief explanation of each option:

• Option A: This is the correct answer. It is the conjugate antisymmetric part of the sequence, as defined above.
• Option B: This is not the correct answer. It is the conjugate symmetric part of the sequence, which is defined as follows:

$$x_{an} = \overline{x_{n}}$$

• Option C: This is not the correct answer. It is the real part of the sequence.
• Option D: This is not the correct answer. It is the imaginary part of the sequence.