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)Responses16±2i16 plus or minus 2 i16±2i2–√16 plus or minus 2 i Start Root 2 End Root4±2i2–√4 plus or minus 2 i Start Root 2 End Root−4±2i

Answer 1

To solve the equation \( 2(x - 16)^2 = -8 \), we first isolate the squared term:

1. Divide both sides by 2: \[ (x - 16)^2 = -4 \]

2. Taking the square root of both sides gives: \[ x - 16 = \pm \sqrt{-4} \]

3. We know that \( \sqrt{-4} = \sqrt{4} \cdot i = 2i \). Therefore, we have: \[ x - 16 = \pm 2i \]

4. Now, solve for \( x \): \[ x = 16 \pm 2i \]

Thus, the solutions can be expressed in standard form as: \[ x = 16 + 2i \quad \text{and} \quad x = 16 - 2i \]

So the solution to the equation in the form \( a \pm bi \) is: \[ \boxed{16 \pm 2i} \]