To find the result of subtracting [tex]\( 8 + 7i \)[/tex] from [tex]\( 4 - 16i \)[/tex], follow these steps:
1. Write down the complex numbers:
[tex]\[ a = 4 - 16i \][/tex]
[tex]\[ b = 8 + 7i \][/tex]
2. Subtract the second complex number from the first:
[tex]\[ (4 - 16i) - (8 + 7i) \][/tex]
3. Separate the real parts and the imaginary parts:
[tex]\[ (4 - 8) + (-16i - 7i) \][/tex]
4. Perform the arithmetic for the real parts:
[tex]\[ 4 - 8 = -4 \][/tex]
5. Perform the arithmetic for the imaginary parts:
[tex]\[ -16i - 7i = -23i \][/tex]
6. Combine the results:
[tex]\[ -4 - 23i \][/tex]
Therefore, the result of the subtraction is [tex]\( -4 - 23i \)[/tex].
The correct answer is:
D. [tex]\(-4 - 23i\)[/tex]
