Question

The solution to a problem involving a complex number is - 4 + 32i. Which of the following expressions could be the problem? Select all that apply.

Answer 1

In simplifying complex numbers, i^2 = - 1

Looking at the given options, the only expression that could be the problem is option C.

We can check by simplifying. We would multiply each term in the first bracket by each term in the second bracket. It beomes

(- 2 - 4i)(- 6 - 4i) = (- 2 * - 6) + (- 2 * - 4i) + (- 4i * - 2) + (- 4i * - 4i)

= 12 + 8i + 24i + 16i^2

= 12 + 8i + 24i + 16(-1)

= 12 + 32i - 16

= 12 - 16 + 32i

= - 4 + 32i

Therefore, option C is the correct answer