Use the imaginary number \( i \) to rewrite the expression below as a complex number. Simplify all radicals. \[ -\sqrt{-32} \]

To rewrite the expression \(-\sqrt{-32}\) using the imaginary unit \(i\), we start by recognizing that \(-\sqrt{-32}\) can be expressed as \(-\sqrt{32} \cdot \sqrt{-1}\), where \(\sqrt{-1} = i\). Thus, we can rewrite it as: \[ -\sqrt{-32} = -\sqrt{32} \cdot i \] Next, we simplify \(\sqrt{32}\). Since \(32 = 16 \times 2\), we can simplify this further: \[ \sqrt{32} = \sqrt{16 \cdot 2} = \sqrt{16} \cdot \sqrt{2} = 4\sqrt{2} \] Now we can substitute this back into our expression: \[ -\sqrt{-32} = -4\sqrt{2} \cdot i \] So the final answer as a complex number is: \[ -4\sqrt{2}i \]