Additive inverse of complex number `-4-7i` is:

Options

A. `4+7i`
B. `-4+7i`
C. `-4-7i`
D. none of these

Answer

To find the additive inverse of the complex number \(-4 - 7i\), we need to determine a complex number that, when added to \(-4 - 7i\), results in zero.

### Step-by-Step Solution:

1. **Understand the concept of additive inverse**: The additive inverse of a number \(z\) is a number \(k\) such that \(z + k = 0\).

2. **Identify the given complex number**: Here, the complex number is \(z = -4 - 7i\).

3. **Set up the equation for the additive inverse**: We need to find \(k\) such that:
\[ (-4 - 7i) + k = 0 \]

4. **Rearrange the equation to find \(k\)**: To isolate \(k\), we can rearrange the equation:
\[ k = -(-4 - 7i) \]

5. **Simplify the expression for \(k\)**: When we simplify the right side, we get:
\[ k = 4 + 7i \]

6. **Conclusion**: Therefore, the additive inverse of the complex number \(-4 - 7i\) is:
\[ 4 + 7i \]

### Final Answer:
The additive inverse of the complex number \(-4 - 7i\) is \(4 + 7i\).