1. The problem is to rewrite the expression $\sqrt{-24}$ as a complex number and simplify all radicals. 2. Recall that the imaginary unit $i$ is defined as $i = \sqrt{-1}$. 3. Using this, we can rewrite $\sqrt{-24}$ as $\sqrt{24 \times -1} = \sqrt{24} \times \sqrt{-1} = \sqrt{24} \times i$. 4. Next, simplify $\sqrt{24}$. Since $24 = 4 \times 6$, we have $\sqrt{24} = \sqrt{4 \times 6} = \sqrt{4} \times \sqrt{6} = 2\sqrt{6}$. 5. Substitute back to get $\sqrt{-24} = 2\sqrt{6} \times i = 2i\sqrt{6}$. 6. Therefore, the expression $\sqrt{-24}$ rewritten as a complex number is $2i\sqrt{6}$.