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]
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]
