Rewrite this imaginary number using \( i \) and then select your answer from the choices. Make sure your answer is fully simplified. \[ \sqrt{-45} \]

To rewrite \( \sqrt{-45} \) using \( i \), first, we can factor out the negative sign: \[ \sqrt{-45} = \sqrt{45} \cdot \sqrt{-1} = \sqrt{45} \cdot i. \] Next, we can simplify \( \sqrt{45} \). Since \( 45 = 9 \times 5 \), we have: \[ \sqrt{45} = \sqrt{9 \cdot 5} = \sqrt{9} \cdot \sqrt{5} = 3\sqrt{5}. \] Putting this all together, we find: \[ \sqrt{-45} = 3\sqrt{5} \cdot i. \] Thus, the simplified form of \( \sqrt{-45} \) is \( 3\sqrt{5}i \).