Multiply. Show your work.
(Type your answer in the form a+bi.)
(7 + 2i)(8 + i)
To multiply (7 + 2i)(8 + i), we can use the foil method:
(7 + 2i)(8 + i) = 7(8) + 7(i) + 2i(8) + 2i(i)
= 56 + 7i + 16i + 2i^2
Remember that i^2 is defined as -1, so we can simplify further:
= 56 + 7i + 16i - 2
= (56 - 2) + (7i + 16i)
= 54 + 23i
Therefore, the answer is 54 + 23i.