The Existence of Imaginary Numbers Quick Check

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**