Let's solve the problem step by step.
We are given two complex numbers, [tex]\(9 + 6i\)[/tex] and [tex]\(1 + 3i\)[/tex], and we need to perform the subtraction operation on them:
[tex]\[ (9 + 6i) - (1 + 3i) \][/tex]
To subtract two complex numbers, we subtract the real parts and the imaginary parts separately.
1. Subtract the real parts:
[tex]\[ 9 - 1 = 8 \][/tex]
2. Subtract the imaginary parts:
[tex]\[ 6i - 3i = 3i \][/tex]
Thus, the result of the subtraction is:
[tex]\[ 8 + 3i \][/tex]
Therefore, the correct answer is:
C. [tex]\(8 + 3i\)[/tex]
