1. The problem asks to find the value of $\sqrt{-121}$. 2. Recall that the square root of a negative number involves the imaginary unit $i$, where $i = \sqrt{-1}$. 3. We can rewrite $\sqrt{-121}$ as $\sqrt{-1 \times 121}$. 4. Using the property of square roots, $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$, we get: $$\sqrt{-121} = \sqrt{-1} \times \sqrt{121}$$ 5. Substitute $\sqrt{-1} = i$ and $\sqrt{121} = 11$: $$\sqrt{-121} = i \times 11 = 11i$$ 6. Therefore, the correct answer is $11i$.