%5E2*(-8i)%5E2.jpeg "(sqrt 3)^2*(-8i)^2")
Simplifying $(\sqrt{3})^2 \cdot (-8i)^2$
This expression involves simplifying powers of imaginary numbers and radicals. Here's a step-by-step solution:
1. Simplifying the radicals:
- $(\sqrt{3})^2 = 3$ (The square of a square root cancels out)
2. Simplifying the imaginary powers:
- (-8i)² = (-8)² * (i)² = 64 * (-1) = -64
- Remember that i² = -1
3. Multiplying the results:
- 3 * (-64) = -192
Therefore, the simplified form of $(\sqrt{3})^2 \cdot (-8i)^2$ is -192.