Final answer:
The expression 5i^4 + 2i^3 - 81 simplifies to -76 - 2i, after acknowledging that i^4 equals 1 and i^3 equals -i.
Step-by-step explanation:
The question provided calls for the simplification of the mathematical expression 5i^4 + 2i^3 - 81. To simplify it, recall that i is the imaginary unit where i^2 = -1. Consequently, i^4, which is (i^2)^2, equals 1. For i^3, this can be rewritten as i^2 × i, which simplifies to -i. Therefore, the expression simplifies to 5×1 + 2×(-i) - 81, which further simplifies to 5 - 2i - 81. After combining like terms, the final answer is -76 - 2i.