1. The problem is to rewrite the expression $\sqrt{-80}$ 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 $\sqrt{-80}$ as $\sqrt{80 \times -1} = \sqrt{80} \times \sqrt{-1} = \sqrt{80} \times i$. 4. Next, simplify $\sqrt{80}$. Since $80 = 16 \times 5$, we have: $$\sqrt{80} = \sqrt{16 \times 5} = \sqrt{16} \times \sqrt{5} = 4\sqrt{5}$$ 5. Substitute back to get: $$\sqrt{-80} = 4\sqrt{5} \times i = 4i\sqrt{5}$$ 6. Therefore, the expression $\sqrt{-80}$ rewritten as a complex number is: $$4i\sqrt{5}$$