Question

type the correct answer in the box. simplify the following expression into the form a + bi, where a and b are rational numbers. (3 + 7i)(-2 - 2i) - 4i(5 - 9i)

Explanation:

Step1: Multiply first complex pair

$$(3 + 7i)(-2 - 2i) = 3(-2) + 3(-2i) + 7i(-2) + 7i(-2i)$$
$$= -6 - 6i - 14i - 14i^2$$
Since $i^2 = -1$, substitute:
$$= -6 - 20i - 14(-1) = -6 - 20i + 14 = 8 - 20i$$

Step2: Multiply the second term

$$4i(5 - 9i) = 4i(5) + 4i(-9i) = 20i - 36i^2$$
Substitute $i^2 = -1$:
$$= 20i - 36(-1) = 36 + 20i$$

Step3: Subtract the two results

$$(8 - 20i) - (36 + 20i) = 8 - 20i - 36 - 20i$$
Combine like terms:
$$= (8 - 36) + (-20i - 20i) = -28 - 40i$$

Answer:

$-28 - 40i$