Use the imaginary number \( i \) to rewrite the expression below as a complex number. Simplify all radicals. \[ -\sqrt{-23} \]

To rewrite the expression \( -\sqrt{-23} \) as a complex number using the imaginary unit \( i \), follow these steps: 1. **Understand the Imaginary Unit \( i \):** The imaginary unit is defined as \( i = \sqrt{-1} \). This allows us to express the square root of negative numbers in terms of \( i \). 2. **Rewrite the Square Root:** \[ \sqrt{-23} = \sqrt{23} \cdot \sqrt{-1} = \sqrt{23} \cdot i = i\sqrt{23} \] 3. **Include the Negative Sign:** \[ -\sqrt{-23} = -i\sqrt{23} \] 4. **Express as a Complex Number:** A complex number is typically written in the form \( a + bi \), where \( a \) is the real part and \( b \) is the imaginary part. In this case, the expression \( -i\sqrt{23} \) can be written as: \[ 0 - i\sqrt{23} \quad \text{or simply} \quad -i\sqrt{23} \] **Final Answer:** \[ -\,i\,\sqrt{23} \]