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