Question

multiply:
(2 - 6i)(-4 + 3i)
a. -26 - 30i
b. -26 + 30i
c. 10 - 30i
d. 10 + 30i

Explanation:

Step1: Apply FOIL method

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

Step2: Calculate each term

$= -8 + 6i + 24i - 18i^2$

Step3: Substitute $i^2=-1$

$= -8 + 6i + 24i - 18(-1)$

Step4: Simplify real and imaginary parts

$= -8 + 18 + (6i + 24i)$
$= 10 + 30i$

Answer:

D. $10+30i$