Question

simplify.
(5 + 2i)(4 − i)
write your answer in the form a + bi.

Explanation:

Step1: Expand using FOIL method

$(5+2i)(4-i) = 5\times4 +5\times(-i) +2i\times4 +2i\times(-i)$

Step2: Compute each term

$=20 -5i +8i -2i^2$

Step3: Substitute $i^2=-1$

$=20 +3i -2\times(-1) = 20 +3i +2$

Step4: Combine real terms

$=22 +3i$

Answer:

$22 + 3i$