Question

perform the indicated operations.
(4 - 3i)(3 - i) - (2 - i)(2 + i)
(4 - 3i)(3 - i) - (2 - i)(2 + i) =
(simplify your answer. type your answer in the form a + bi.)

Explanation:

Step1: Expand first complex product

Use FOIL method: $(a+bi)(c+di)=ac+adi+bci+bdi^2$, $i^2=-1$
$$(4-3i)(3-i)=4*3 + 4*(-i) + (-3i)*3 + (-3i)*(-i)=12-4i-9i+3i^2=12-13i+3(-1)=9-13i$$

Step2: Expand second complex product

Use difference of squares: $(a-bi)(a+bi)=a^2+b^2$
$$(2-i)(2+i)=2^2+1^2=4+1=5$$

Step3: Subtract the two results

Subtract the second product from the first
$$(9-13i)-5=4-13i$$

Answer:

$4 - 13i$