1. The problem is to rewrite the expression $\sqrt{-57}$ using the imaginary number $i$ and simplify all radicals. 2. Recall that the imaginary unit $i$ is defined as $i = \sqrt{-1}$. 3. Using this definition, we can rewrite $\sqrt{-57}$ as $\sqrt{57 \times -1} = \sqrt{57} \times \sqrt{-1} = \sqrt{57} \times i$. 4. Since $\sqrt{57}$ cannot be simplified further (57 is $3 \times 19$, both prime), the simplified form is $i\sqrt{57}$. 5. Therefore, the expression $\sqrt{-57}$ rewritten as a complex number is $i\sqrt{57}$.