Use the imaginary number \( i \) to rewrite the expression below as a complex number. Simplify all radicals. \( -18-\sqrt{-69} \)

To express the given expression \( -18 - \sqrt{-69} \) as a complex number using the imaginary unit \( i \), follow these steps: 1. **Identify the Imaginary Part:** The term \( \sqrt{-69} \) involves the square root of a negative number, which can be expressed using the imaginary unit \( i \): \[ \sqrt{-69} = i \sqrt{69} \] 2. **Rewrite the Expression:** Substitute the imaginary part back into the original expression: \[ -18 - \sqrt{-69} = -18 - i \sqrt{69} \] 3. **Simplify if Possible:** The radical \( \sqrt{69} \) cannot be simplified further since 69 factors into \( 3 \times 23 \), neither of which are perfect squares. Thus, the expression in its simplified complex form is: \[ -18 - i \sqrt{69} \] **Answer:** \(\boxed{-18\ -\ i\,\sqrt{69}}\)