%5E3.jpeg "(2i^3)^3")
Simplifying (2i^3)^3
This problem involves simplifying a complex number raised to a power. Let's break it down step by step:
1. Simplifying the inner exponent:
- i^3 = i^2 * i = -1 * i = -i
- Therefore, (2i^3) = (2 * -i) = -2i
2. Applying the outer exponent:
- (-2i)^3 = (-2i) * (-2i) * (-2i) = 8i^3
3. Simplifying i^3:
- As we know, i^3 = -i
4. Final answer:
- 8i^3 = 8 * -i = -8i
Therefore, (2i^3)^3 simplifies to -8i.