Final answer:
After distributing -2i to each term within the parentheses and then subtracting the second complex number, the answer should be 56 - 8i, which is not an option listed. There appears to be an error with the provided choices.
Step-by-step explanation:
The question asks to simplify the expression -2i (9-31i) - (6-10i) and write the result as a complex number in standard form, which is a + bi, where a is the real part and bi is the imaginary part.
First, distribute -2i to both terms in the parenthesis (9 - 31i):
- -2i × 9 = -18i
- -2i × (-31i) = 62
Next, subtract the second complex number (6 - 10i) from the result:
- 62 - 6 = 56
- -18i - (-10i) = -8i
Combining the real and imaginary components, we get 56 - 8i, which is not an option in the multiple-choice list provided. It seems there is an error either in the question or the options given. However, the process described here is correct for combining complex numbers.