To solve the equation \(x^2 + 4 = 0\), we can rearrange it:
\[ x^2 = -4 \]
To find \(x\), we take the square root of both sides. The square root of a negative number involves imaginary numbers:
\[ x = \pm \sqrt{-4} = \pm \sqrt{4}i = \pm 2i \]
Thus, the solutions for \(x\) are \(2i\) and \(-2i\), which are imaginary numbers.
Therefore, the correct response is:
imaginary