Simplify the expression. Show your work.
(Type your answer in the form a+bi.)
(7 + i)(5 - 4i)
To multiply the two complex numbers, we can use the FOIL method.
(7 + i)(5 - 4i) = 7*5 + 7*(-4i) + i*5 + i*(-4i)
= 35 - 28i + 5i - 4i^2
Since i^2 = -1, we can simplify further:
35 - 28i + 5i - 4i^2 = 35 - 28i + 5i - 4(-1)
= 35 - 28i + 5i + 4
= 39 - 23i
Therefore, the simplified expression is 39 - 23i.