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)%0D%0AResponses%0D%0A%0D%0A−4±2i%0D%0Anegative 4 plus or minus 2 i%0D%0A%0D%0A4±2i2–√%0D%0A4 plus or minus 2 i Start Root 2 End Root%0D%0A%0D%0A16±2i%0D%0A16 plus or minus 2 i%0D%0A%0D%0A16±2i2–√

Answer 1

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

\[ (x - 16)^2 = -4 \]

Next, we take the square root of both sides:

\[ x - 16 = \pm \sqrt{-4} \]

The square root of \(-4\) can be expressed using imaginary numbers. We know that:

\[ \sqrt{-4} = \sqrt{4} \cdot \sqrt{-1} = 2i \]

So, we have:

\[ x - 16 = \pm 2i \]

Next, we solve for \(x\) by adding 16 to both sides:

\[ x = 16 \pm 2i \]

This yields the solutions:

\[ x = 16 + 2i \quad \text{and} \quad x = 16 - 2i \]

In standard form \(a \pm bi\), the correct answer is:

\[ 16 \pm 2i \]

Thus, the correct choice from the options provided is:

16±2i