Question

Use the properties of complex numbers to simplify (9+sqrt(-4)+(-9-sqrt(-16)

.

A
−2i

B
18-\sqrt{-20}
​


C
18−2i

D
6i

Answer 1

To simplify the expression \(9+\sqrt{-4}+(-9-\sqrt{-16})\), we'll start by addressing the square roots of the negative numbers involved.

1. **Calculating \(\sqrt{-4}\)**:
\[
\sqrt{-4} = \sqrt{4} \cdot \sqrt{-1} = 2i
\]

2. **Calculating \(\sqrt{-16}\)**:
\[
\sqrt{-16} = \sqrt{16} \cdot \sqrt{-1} = 4i
\]

3. **Substituting these values into the original expression**:
\[
9 + 2i + (-9 - 4i)
\]

4. **Simplifying the expression**:
- Combine the real parts:
\[
9 - 9 = 0
\]
- Combine the imaginary parts:
\[
2i - 4i = -2i
\]

5. **Final result**:
\[
0 - 2i = -2i
\]

Thus, the simplified expression is \(-2i\).

The correct answer is **A) -2i**.