Use the imaginary number \( i \) to rewrite the expression below as a complex number. Simplify all radicals. \( -18+\sqrt{-33} \) \begin{tabular}{|c|c|}\hline \\ \hline\( i \) & \\ \hline\end{tabular}

To rewrite the expression \( -18 + \sqrt{-33} \) as a complex number using the imaginary unit \( i \), follow these steps: 1. **Identify the Imaginary Part:** The term \( \sqrt{-33} \) involves a square root of a negative number. Recall that \( \sqrt{-1} = i \). Therefore: \[ \sqrt{-33} = \sqrt{33} \cdot \sqrt{-1} = \sqrt{33} \, i \] 2. **Rewrite the Expression:** Substitute \( \sqrt{-33} \) with \( \sqrt{33} \, i \) in the original expression: \[ -18 + \sqrt{-33} = -18 + \sqrt{33} \, i \] 3. **Final Complex Number:** The expression is now written in standard form for a complex number \( a + b i \), where \( a = -18 \) and \( b = \sqrt{33} \). \[ -18 + \sqrt{33}\,i \]