Use the imaginary number \( i \) to rewrite the expression below as a complex number. Simplify all radicals. \( \sqrt{-33} \)

To rewrite the expression \( \sqrt{-33} \) as a complex number using the imaginary unit \( i \), follow these steps: 1. **Understand the Imaginary Unit**: - The imaginary unit \( i \) is defined as \( i = \sqrt{-1} \). 2. **Rewrite the Square Root of a Negative Number**: - \( \sqrt{-33} \) can be expressed as \( \sqrt{33} \times \sqrt{-1} \). - Using the definition of \( i \), this becomes \( \sqrt{33} \times i \). 3. **Simplify**: - The expression simplifies to \( \sqrt{33}\,i \). **Final Answer:** \[ \sqrt{33}\,i \]