\( 1 \leftarrow \quad \) Perform the indicated operations and write the result in standard form. \( -\frac{-8+\sqrt{-20}}{24} \)

To simplify the expression and write it in standard form \( a + bi \), follow these steps: Given expression: \[ -\frac{-8 + \sqrt{-20}}{24} \] 1. **Simplify the Square Root of a Negative Number:** \[ \sqrt{-20} = \sqrt{20} \cdot i = 2\sqrt{5} \, i \] 2. **Substitute Back into the Expression:** \[ -\frac{-8 + 2\sqrt{5} \, i}{24} \] 3. **Distribute the Negative Sign:** \[ \frac{8 - 2\sqrt{5} \, i}{24} \] 4. **Separate the Real and Imaginary Parts:** \[ \frac{8}{24} - \frac{2\sqrt{5}}{24} \, i \] 5. **Simplify the Fractions:** \[ \frac{1}{3} - \frac{\sqrt{5}}{12} \, i \] **Final Answer:** \[ \frac{1}{3} - \frac{\sqrt{5}}{12}\,i \]