What is the difference of the complex numbers below?

[tex]\[ (11 - 3i) - (4 + 5i) \][/tex]

A. [tex]\( 15 - 8i \)[/tex]
B. [tex]\( 7 - 8i \)[/tex]
C. [tex]\( 15 - 2i \)[/tex]
D. [tex]\( 7 - 2i \)[/tex]



Answer :

To find the difference between the two complex numbers [tex]\((11 - 3i)\)[/tex] and [tex]\((4 + 5i)\)[/tex], follow these steps:

1. Identify the real and imaginary parts of each complex number:
- The first complex number, [tex]\(11 - 3i\)[/tex], has a real part of 11 and an imaginary part of [tex]\(-3i\)[/tex].
- The second complex number, [tex]\(4 + 5i\)[/tex], has a real part of 4 and an imaginary part of [tex]\(5i\)[/tex].

2. Subtract the real parts:
[tex]\[ 11 - 4 = 7 \][/tex]

3. Subtract the imaginary parts:
[tex]\[ -3i - 5i = -8i \][/tex]

4. Combine the results from the subtractions to form the resulting complex number:
[tex]\[ 7 - 8i \][/tex]

Thus, the difference of the given complex numbers is:
[tex]\[ (11 - 3i) - (4 + 5i) = 7 - 8i \][/tex]

So, the correct answer is:
[tex]\[ \boxed{7 - 8i} \][/tex]

Therefore, the correct choice from the given options is:
[tex]\[ \boxed{B} \][/tex]