Question: Write the number in standard form.
$$\frac{-10 + \sqrt{-40}}{2}$$
(Simplify your answer. Type your answer in the form $a + bi$. Type an exact answer, using radicals as needed.)
1. **State the problem:** Simplify the expression $$\frac{-10 + \sqrt{-40}}{2}$$ and write it in the form $a + bi$.
2. **Recall the formula and rules:** When simplifying square roots of negative numbers, use $$\sqrt{-1} = i$$, where $i$ is the imaginary unit.
3. **Simplify the square root:**
$$\sqrt{-40} = \sqrt{-1 \times 40} = \sqrt{-1} \times \sqrt{40} = i \sqrt{40}$$
4. **Simplify $$\sqrt{40}$$:**
$$\sqrt{40} = \sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10} = 2 \sqrt{10}$$
5. **Substitute back:**
$$\frac{-10 + i 2 \sqrt{10}}{2}$$
6. **Divide numerator terms by denominator:**
$$\frac{-10}{2} + \frac{i 2 \sqrt{10}}{2} = -5 + i \sqrt{10}$$
7. **Show cancellation step explicitly:**
$$\frac{\cancel{2} i \sqrt{10}}{\cancel{2}} = i \sqrt{10}$$
**Final answer:** $$-5 + i \sqrt{10}$$