Simplify the expression. Show your work.
(Type your answer in the form a+bi.)
(3 + i)(8 + 5i)
To simplify the given expression, we can use the distributive property to multiply the two binomials:
(3 + i)(8 + 5i)
= 3(8) + 3(5i) + i(8) + i(5i)
= 24 + 15i + 8i + 5i^2
Remember that i^2 is equal to -1, so we can substitute -1 for i^2:
24 + 15i + 8i + 5i^2
= 24 + (15i + 8i) + 5(-1)
= 24 + 23i - 5
= 19 + 23i
Therefore, the simplified expression is 19 + 23i.