To find the value of (8+9i)(8+9i), we can use the FOIL method (First, Outer, Inner, Last):
(8+9i)(8+9i) = 8(8) + 8(9i) + 9i(8) + 9i(9i)
Simplifying each term, we get:
64 + 72i + 72i + 81i^2
Note that i^2 is equal to -1, so we can substitute -1 for i^2:
64 + 72i + 72i - 81
Combining like terms, we get:
-17 + 144i
Therefore, (8+9i)(8+9i) = -17 + 144i.