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

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UpStudy AI · Accepted Answer

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:**
$$
\frac{1}{3} - \frac{\sqrt{5}}{12}\,i
$$
The simplified form of the expression is $$ \frac{1}{3} - \frac{\sqrt{5}}{12}i $$.

Perform the indicated operations and write the result in standard form.

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