Use the imaginary number \( i \) to rewrite the expression below as a complex number. Simplify all radicals. \[ 9-\sqrt{-93} \]

To rewrite the expression \( 9 - \sqrt{-93} \) as a complex number using the imaginary unit \( i \), follow these steps: 1. **Understand the Imaginary Unit:** The imaginary unit \( i \) is defined as \( i = \sqrt{-1} \). This allows us to express square roots of negative numbers in terms of \( i \). 2. **Rewrite the Square Root of a Negative Number:** \[ \sqrt{-93} = \sqrt{93} \cdot \sqrt{-1} = \sqrt{93} \cdot i \] 3. **Substitute Back into the Original Expression:** \[ 9 - \sqrt{-93} = 9 - \sqrt{93} \cdot i \] 4. **Simplify the Expression:** The expression is already in its simplest form since \( \sqrt{93} \) cannot be simplified further (93 factors into 3 and 31, both of which are prime numbers). **Final Answer:** \[ 9 - i\,\sqrt{93} \]