Consider the remainder of the division of the power exponent of i by 4.
For a remainder r equal to 0, 1, 2 or 3, we have a power equal to 1, i, -1 or -i respectively, therefore:
\(8i^7+6i^5-5i^3-3i^2-7i-9 =\)
\(8*(-i) + 6*i - 5*(-i) - 3*(-1) - 7i - 9 =\)
\(- 8i + 6i + 5i + 3 - 7i - 9 =\)
\(3 - 9 - 8i + 6i + 5i- 7i =\)
\(=\boxed{- 6 - 4i}\)
Answer:
\(\boxed{- 6 - 4i}\)
