e the imaginary number i to rewrite the expression below as a complex number. Simp radicals. \( -\sqrt{-66} \)

To express the expression \(-\sqrt{-66}\) as a complex number using the imaginary unit \(i\) (where \(i = \sqrt{-1}\)), follow these steps: 1. **Understand the Imaginary Unit (\(i\)):** The imaginary unit \(i\) is defined as: \[ i = \sqrt{-1} \] This allows us to handle square roots of negative numbers by expressing them in terms of \(i\). 2. **Rewrite \(-\sqrt{-66}\) Using \(i\):** Start with the original expression: \[ -\sqrt{-66} \] Break down the square root of the negative number: \[ \sqrt{-66} = \sqrt{66 \times (-1)} = \sqrt{66} \times \sqrt{-1} \] Substitute \(\sqrt{-1}\) with \(i\): \[ \sqrt{-66} = \sqrt{66} \times i = i\sqrt{66} \] Now, include the negative sign from the original expression: \[ -\sqrt{-66} = -i\sqrt{66} \] 3. **Final Complex Number:** The expression \(-\sqrt{-66}\) expressed as a complex number is: \[ -i\sqrt{66} \] This is in the standard form \(a + bi\), where \(a = 0\) and \(b = -\sqrt{66}\). 4. **Summary:** \[ -\sqrt{-66} = -i\sqrt{66} \] This represents the original expression as a complex number with an imaginary component.