Question

perform the indicated operations.
(3 - 4i)(1 - i) - (4 - i)(4 + i)
simplify your answer. type your answer in the form a + bi.)

Explanation:

Step1: Expand first product

$(3-4i)(1-i) = 3(1) + 3(-i) -4i(1) -4i(-i) = 3 - 3i -4i +4i^2$
Since $i^2=-1$, substitute:
$3 -7i +4(-1) = 3 -7i -4 = -1 -7i$

Step2: Expand second product

$(4-i)(4+i) = 4^2 - i^2$ (difference of squares)
Substitute $i^2=-1$:
$16 - (-1) = 16 +1 =17$

Step3: Subtract the two results

$(-1 -7i) - 17 = -1 -17 -7i$

Answer:

$-18 -7i$