We have to simplify complex numbers and I was wondering whether I did these problems correctly.

1. 4i^2-2i^3 = -4+2i
2. (-i)^3 = i
3. (the square root of a -2)^6= -8
4.1/(2i)^3 = i/8

1. right

2. right
3. [sqrt(-2)]^6 = -8 yes if that is the question
4. right

To check whether you simplified the complex numbers correctly, we can start by breaking down each problem and simplifying it step-by-step.

1. 4i^2 - 2i^3 = -4 + 2i
First, we simplify the powers of i:
i^2 = -1 (by definition)
i^3 = i^2 * i = -1 * i = -i

Plugging these values back into the equation, we have:
4 * (-1) - 2 * (-i) = -4 + 2i
-4 + 2i = -4 + 2i

Since both sides of the equation are equal, your answer is correct.

2. (-i)^3 = i
Here, we need to simplify the power of -i:
(-i)^3 = -i^3 = -(-i) = i

So, your answer is correct.

3. (√a - 2)^6 = -8
We don't have a specific value for "a." To simplify this problem, let's assume a value for "a" and see if we get -8.

If we assume a = 16, the equation becomes:
(√16 - 2)^6 = (4 - 2)^6 = 2^6 = 64

Since 64 is not equal to -8, this means that the equation (√a - 2)^6 = -8 has no solution. Please double-check your calculations or any missing information to see if there's another way to solve this problem.

4. 1 / (2i)^3 = i/8
We can simplify this by first calculating the cube of (2i):
(2i)^3 = (2i)(2i)(2i) = 4i^2(2i) = 4(-1)(2i) = -8i

Now, we can substitute this value back into the original equation:
1 / (-8i) = i/8

Your answer is correct.

Overall, your answers for problems 1, 2, and 4 are correct. However, there seems to be an issue with problem 3. Please review the problem and any missing information to find a solution.