Given Sequence:
The given sequence is x[n] = [-4-j5, 1+j2, 4].

Conjugate Anti-symmetric Part:
To find the conjugate anti-symmetric part of the sequence, we need to compute the conjugate of each element and then subtract it from the negation of its reversed sequence.

Let's calculate the conjugate of each element:

- Conjugate of -4-j5 = -4+j5
- Conjugate of 1+j2 = 1-j2
- Conjugate of 4 = 4

Now, let's reverse the sequence and negate it:

Reversed sequence = [4, 1+j2, -4-j5]
Negation of reversed sequence = [-4, -(1+j2), -(4+j5)]
= [-4, -1-j2, -4-j5]

Next, we subtract the conjugate of each element from the negation of the reversed sequence:

Conjugate Anti-symmetric part = [-4+j5 - (-4), 1-j2 - (-1-j2), 4 - (-4-j5)]
= [-4+j5 + 4, 1-j2 + 1+j2, 4 + 4+j5]
= [j5, 2j2, 8+j5]

Correct Answer:
The correct answer is option A: [-4-j2.5, j2, 4-j2.5].

Explanation:
In the given options, let's check each option by comparing it with the calculated Conjugate Anti-symmetric part:

a) [-4-j2.5, j2, 4-j2.5]
Comparing this option with the calculated Conjugate Anti-symmetric part, we can see that it matches.

b) [-j2.5, 1, j2.5]
Comparing this option with the calculated Conjugate Anti-symmetric part, we can see that the first element is not correct.

c) [-j5, j2, 0]
Comparing this option with the calculated Conjugate Anti-symmetric part, we can see that the first and third elements are not correct.

d) [-4, 1, 4]
Comparing this option with the calculated Conjugate Anti-symmetric part, we can see that all the elements are not correct.

Therefore, the correct answer is option A: [-4-j2.5, j2, 4-j2.5].