\( 1 \leftarrow \) Perform the indicated operations and write the result in standard form. \( \frac{-12+\sqrt{-45}}{24} \) \( \frac{-12+\sqrt{-45}}{24}=\square \) (Type an exact answer, using radicals as needed. Type your answer in the form a + bi.)

To perform the indicated operations on the expression \( \frac{-12+\sqrt{-45}}{24} \), we first need to simplify \( \sqrt{-45} \). Since \( -45 = -1 \times 45 \), we can express the square root as: \[ \sqrt{-45} = \sqrt{-1} \times \sqrt{45} = i \sqrt{45} = i \sqrt{9 \times 5} = i \cdot 3\sqrt{5} = 3i\sqrt{5} \] Now, substituting back into the original expression: \[ \frac{-12 + \sqrt{-45}}{24} = \frac{-12 + 3i\sqrt{5}}{24} \] Next, we separate the real and imaginary parts: \[ = \frac{-12}{24} + \frac{3i\sqrt{5}}{24} = -\frac{1}{2} + \frac{i\sqrt{5}}{8} \] Thus, the result in standard form \( a + bi \) is: \[ -\frac{1}{2} + \frac{\sqrt{5}}{8}i \] So we have: \[ \frac{-12+\sqrt{-45}}{24} = -\frac{1}{2} + \frac{\sqrt{5}}{8}i \]