Express \( -5 \sqrt{-81} \) as a complex number (in terms of \( i \) ): \( -5 \sqrt{-81}=\square \)

To express \( -5 \sqrt{-81} \) as a complex number, we first need to simplify the square root. The square root of \(-81\) can be rewritten using \(i\) (the imaginary unit) since \(i = \sqrt{-1}\): \[ \sqrt{-81} = \sqrt{81} \cdot \sqrt{-1} = 9i \] Now, substituting this back into the original expression: \[ -5 \sqrt{-81} = -5 \cdot 9i = -45i \] Thus, the expression in terms of \(i\) is: \[ -5 \sqrt{-81} = -45i \]