To solve the equation \( x^2 + 9 = 0 \), we can first isolate \( x^2 \):
\[ x^2 = -9 \]
Next, we take the square root of both sides:
\[ x = \pm \sqrt{-9} \]
This simplifies to:
\[ x = \pm 3i \]
Thus, the solutions are \( 3i \) and \( -3i \).
Among the given options, the correct solution is:
\({3i, -3i}\)
So the answer is:
\({3i, -3i}\)