1. The problem is to rewrite the expression $\sqrt{-39}$ 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 $\sqrt{-39}$ as $\sqrt{39 \times -1} = \sqrt{39} \times \sqrt{-1} = \sqrt{39} \times i$. 4. Since $39$ is $3 \times 13$ and neither 3 nor 13 is a perfect square, $\sqrt{39}$ cannot be simplified further. 5. Therefore, the simplified complex number form is $i \sqrt{39}$. Final answer: $$\sqrt{-39} = i \sqrt{39}$$