Which is the solution to the equation 2(x−16)2=−8 , re-expressed as a complex number in the standard form a±bi ?(1 point)

Question

1. 16±2i
2. 16±2i√2
3. -4±2i
4. 4±2i√2

Answer 1

To solve the equation, let's start by dividing both sides by 2:

(x - 16)² = -4

Next, let's take the square root of both sides to eliminate the exponent of 2:

√((x - 16)²) = ±√(-4)

Now, we can simplify the radical on the right side:

(x - 16) = ±√(4) * √(-1)

The square root of 4 is 2:

(x - 16) = ±2 * √(-1)

Now, let's express the square root of -1 as "i":

(x - 16) = ±2i

Finally, let's solve for x:

x = 16 ± 2i

So the solution to the equation in the standard form a ± bi is 16 ± 2i.

Therefore, the correct answer is option 1. 16±2i.