Final answer:
The solution to the complex number expression 8 + i(8 - i) - 4i(-2i + 6) is 17 + 32i.
Step-by-step explanation:
The student is asking for the solution to a complex number expression: 8 + i(8 - i) - 4i(-2i + 6).
First, we should distribute the imaginary unit i inside the parentheses:
- i(8 - i) equals 8i - i^2.
- -4i(-2i + 6) equals 8i^2 - 24i.
Remembering that i^2 equals -1, we substitute this value to simplify the expression further:
- 8i - i^2 becomes 8i - (-1) which is 8i + 1.
- 8i^2 - 24i becomes -8 - 24i because 8i^2 is the same as 8(-1).
Now we combine all the terms:
- 8 + (8i + 1) - (-8 - 24i) equals 8 + 8i + 1 + 8 + 24i which simplifies to 17 + 32i.
The solution to the complex number expression is 17 + 32i.