Use the imaginary number \( i \) to rewrite the expression below as a complex number. Simplify all radicals. \[ 2+\sqrt{-18} \]

To rewrite the expression \( 2 + \sqrt{-18} \) as a complex number, follow these steps: 1. **Express the Square Root of a Negative Number:** The square root of a negative number can be expressed using the imaginary unit \( i \), where \( i = \sqrt{-1} \). \[ \sqrt{-18} = \sqrt{18} \cdot \sqrt{-1} = \sqrt{18} \cdot i \] 2. **Simplify the Radical:** Simplify \( \sqrt{18} \) by factoring out the perfect square. \[ \sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \cdot \sqrt{2} = 3\sqrt{2} \] Therefore, \[ \sqrt{-18} = 3\sqrt{2} \cdot i = 3\sqrt{2}i \] 3. **Combine with the Real Part:** Now, substitute back into the original expression: \[ 2 + \sqrt{-18} = 2 + 3\sqrt{2}i \] So, the expression \( 2 + \sqrt{-18} \) rewritten as a complex number is: \[ 2 + 3\sqrt{2}\,i \] Answer: \(2 + 3\,\sqrt{2}\,i\)