Question

type the correct answer in the box. simplify the given expression into the form ( a + bi ), where a and b are rational numbers. ( 2(-36 - 3i) + (5 + 2i)(12 - 2i) )

Explanation:

Step1: Expand the first term

$2(-36 - 3i) = -72 - 6i$

Step2: Expand the product term

Use FOIL method:
$(5+2i)(12-2i) = 5\times12 + 5\times(-2i) + 2i\times12 + 2i\times(-2i)$
$= 60 - 10i + 24i - 4i^2$
Since $i^2=-1$, substitute:
$= 60 + 14i - 4(-1) = 60 + 14i + 4 = 64 + 14i$

Step3: Add the two results

$(-72 - 6i) + (64 + 14i) = (-72+64) + (-6i+14i)$
$= -8 + 8i$

Answer:

$-8 + 8i$