1. Stating the problem: We need to multiply the complex numbers $11i$ and $-3i$. 2. Recall the rule for multiplying complex numbers: When multiplying, multiply the coefficients and the imaginary units separately. 3. Multiply the coefficients: $11 \times (-3) = -33$. 4. Multiply the imaginary units: $i \times i = i^2$. 5. Recall that $i^2 = -1$. 6. Combine the results: $-33 \times i^2 = -33 \times (-1) = 33$. 7. Final answer: $(11i)(-3i) = 33$.