se the imaginary number \( i \) to rewrite the expression below as a complex number Il radicals. \( -\sqrt{-90} \)

To rewrite the expression \(-\sqrt{-90}\) as a complex number using the imaginary unit \(i\), follow these steps: 1. **Understand the Imaginary Unit**: The imaginary unit \(i\) is defined as \(i = \sqrt{-1}\). This allows us to express the square root of a negative number in terms of \(i\). 2. **Rewrite the Expression**: \[ -\sqrt{-90} = -\sqrt{90} \cdot \sqrt{-1} = -\sqrt{90} \cdot i \] 3. **Simplify \(\sqrt{90}\)**: Factor 90 to simplify the square root: \[ \sqrt{90} = \sqrt{9 \times 10} = \sqrt{9} \cdot \sqrt{10} = 3\sqrt{10} \] 4. **Combine the Results**: Substitute back into the expression: \[ -\sqrt{-90} = -3\sqrt{10} \cdot i \] So, the expression \(-\sqrt{-90}\) rewritten as a complex number is: \[ -3\sqrt{10}\,i \] **Answer:** \(-3\,\sqrt{10}\,i\)