1. The problem asks us to rewrite the expression $\sqrt{-16}$ as a complex number using the imaginary unit $i$. 2. Recall that the imaginary unit $i$ is defined as $i = \sqrt{-1}$. 3. We can rewrite $\sqrt{-16}$ as $\sqrt{16 \times -1}$. 4. Using the property of square roots, $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$, we get: $$\sqrt{-16} = \sqrt{16} \times \sqrt{-1}$$ 5. Simplify $\sqrt{16}$ which is $4$, and $\sqrt{-1}$ is $i$: $$\sqrt{-16} = 4i$$ 6. Therefore, the expression $\sqrt{-16}$ rewritten as a complex number is $4i$. Final answer: $4i$