Use the imaginary number \( i \) to rewrite the expression below as a complex number. Simplify all radicals. \( -8+\sqrt{-40} \)

To rewrite the expression \( -8+\sqrt{-40} \) as a complex number, we first simplify the square root of the negative number. We know that \( \sqrt{-40} = \sqrt{40} \cdot \sqrt{-1} = \sqrt{40} \cdot i \). Now, we simplify \( \sqrt{40} \). The number 40 can be factored into \( 4 \times 10 \), where \( \sqrt{4} = 2 \). Thus, \( \sqrt{40} = \sqrt{4 \cdot 10} = \sqrt{4} \sqrt{10} = 2\sqrt{10} \). Now we can rewrite our expression: \[ -8 + \sqrt{-40} = -8 + 2\sqrt{10}i \] So, the expression simplifies to: \[ -8 + 2\sqrt{10}i \] Thus, the final answer as a complex number is \( -8 + 2\sqrt{10}i \).