Which is the solution to the equation 2(x - 16)^2=-8, re-expressed as a complex number in the standard form a ± bi?

Question

16±2i√2
-4±2i
4±2i√2
16±2i

Answer 1

To solve the equation 2(x - 16)^2 = -8, we can start by dividing both sides by 2:

(x - 16)^2 = -4

Next, we can take the square root of both sides to eliminate the square:

x - 16 = ±√(-4)

Since the square root of a negative number is not a real number, we know that the solution will be a complex number. We can rewrite √(-4) as 2i, where i represents the imaginary unit.

x - 16 = ±2i

Adding 16 to both sides, we have:

x = 16 ± 2i

Therefore, the solution to the equation 2(x - 16)^2 = -8, re-expressed as a complex number in the standard form a ± bi, is 16 ± 2i. The correct answer is 16 ± 2i.

Answer 2

Thanks!

Answer 3

You're welcome! If you have any more questions, feel free to ask.