Question

simplify.
(4 + 5i)(4 − 3i)
write your answer in the form a + bi.

Explanation:

Step1: Expand using FOIL method

$(4+5i)(4-3i) = 4\cdot4 + 4\cdot(-3i) +5i\cdot4 +5i\cdot(-3i)$

Step2: Calculate each term

$=12 -12i +20i -15i^2$

Step3: Substitute $i^2=-1$

$=16 +8i -15(-1) =16 +8i +15$

Step4: Combine real terms

$=31 +8i$

Answer:

$\boldsymbol{31 + 8i}$