To multiply the two complex numbers \((-11 + 8i)\) and \((-1 - 8i)\), we can use the distributive property (also known as the FOIL method for binomials).
\[ (-11 + 8i)(-1 - 8i) = (-11)(-1) + (-11)(-8i) + (8i)(-1) + (8i)(-8i) \]
Now, we will calculate each term:
- \((-11)(-1) = 11\)
- \((-11)(-8i) = 88i\)
- \((8i)(-1) = -8i\)
- \((8i)(-8i) = -64i^2\)
Since \(i^2 = -1\), we can replace \(-64i^2\) with \(64\):
\[ (-11 + 8i)(-1 - 8i) = 11 + 88i - 8i + 64 \]
Now, combine the like terms:
\[ (11 + 64) + (88i - 8i) = 75 + 80i \]
Thus, the result of multiplying \((-11 + 8i)\) and \((-1 - 8i)\) is:
\[ \boxed{75 + 80i} \]