Solve each quadratic equation. If roots are not real, use $i$.
$\frac{w^2}{4}+8=0$

• A. $w=\pm 4\sqrt{2}i$
• B. $w=\pm 4i$
• C. $w=\pm 4$
• D. $w=\pm 4\sqrt{2}$

Answer: (A)

Verified step by step guidance

1. Start with the given equation: \(\frac{w^2}{4} + 8 = 0\).
2. Isolate the term with \(w^2\) by subtracting 8 from both sides: \(\frac{w^2}{4} = -8\).
3. Eliminate the denominator by multiplying both sides of the equation by 4: \(w^2 = -8 \times 4\).
4. Simplify the right side to get \(w^2 = -32\).
5. Since \(w^2\) equals a negative number, take the square root of both sides, remembering to include the imaginary unit \(i\) for the square root of a negative number: \(w = \pm \sqrt{-32} = \pm \sqrt{32}i\).