(2i^3)^3

less than a minute read Jun 16, 2024
(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.

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