Question

simplify.
(3 + 2i)(-2 - i)
write your answer in the form a + bi.

Explanation:

Step1: Expand using FOIL method

$(3)(-2) + (3)(-i) + (2i)(-2) + (2i)(-i)$

Step2: Calculate each term

$-6 - 3i - 4i - 2i^2$

Step3: Substitute $i^2=-1$

$-6 - 3i - 4i - 2(-1)$

Step4: Simplify constants and like terms

$-6 + 2 + (-3i - 4i)$
$-4 - 7i$

Answer:

$-4 - 7i$