Final answer:
To simplify the expression (9+2i)(9−2i), use the FOIL method and substitute the value of i^2 to simplify the expression to 85.
Step-by-step explanation:
To simplify the expression (9+2i)(9−2i), we can use the FOIL method, which stands for First, Outer, Inner, Last. Multiply the first terms, then the outer terms, then the inner terms, and finally the last terms.
(9+2i)(9−2i) = 9*9 + 9*(-2i) + 2i*9 + 2i*(-2i)
= 81 - 18i + 18i - 4i^2
= 81 - 4i^2
Since i^2 = -1, we can substitute that value into the expression.
= 81 - 4(-1)
= 81 + 4
= 85
So, the simplified expression is 85.