Use the imaginary number \( i \) to rewrite the expression below as a complex number. Simplify all radicals. \( -19-\sqrt{-99} \)

To express the given expression \( -19 - \sqrt{-99} \) as a complex number using the imaginary unit \( i \), follow these steps: 1. **Identify the Imaginary Component:** The term \( \sqrt{-99} \) involves the square root of a negative number, which can be expressed using the imaginary unit \( i \), where \( i = \sqrt{-1} \). 2. **Rewrite the Square Root of the Negative Number:** \[ \sqrt{-99} = \sqrt{99} \cdot \sqrt{-1} = \sqrt{99} \cdot i \] 3. **Simplify the Radical \( \sqrt{99} \):** Factor 99 to simplify the square root: \[ 99 = 9 \times 11 \] \[ \sqrt{99} = \sqrt{9 \times 11} = \sqrt{9} \cdot \sqrt{11} = 3\sqrt{11} \] Therefore, \[ \sqrt{-99} = 3\sqrt{11} \cdot i = 3\sqrt{11}i \] 4. **Substitute Back into the Original Expression:** \[ -19 - \sqrt{-99} = -19 - 3\sqrt{11}i \] 5. **Express in Standard Complex Number Form:** A complex number is typically written in the form \( a + bi \), where \( a \) is the real part and \( b \) is the imaginary coefficient. Thus, \[ -19 - 3\sqrt{11}i \] is the simplified complex number form of the original expression. **Final Answer:** \[ -19 - 3\,\sqrt{11}\,i \]