Question

4
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: Expand first product

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

Step2: Expand second product

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

Step3: Subtract the two results

Subtract the second expanded term from the first:
$$(8 -20i) - (36 +20i) = 8 -20i -36 -20i$$

Step4: Combine like terms

Combine real and imaginary parts:
$$(8-36) + (-20i-20i) = -28 -40i$$

Answer:

$-28 - 40i$