Find the multiplicative inverse of each of the following complex numbers when it exists.
`-16`

Answer

To find the multiplicative inverse of the complex number \(-16\), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Complex Number**:
The complex number given is \(-16\). In terms of complex numbers, we can express it as:
\[ -16 + 0i \]

2. **Understanding the Multiplicative Inverse**:
The multiplicative inverse of a complex number \(z\) is defined as a number \(w\) such that:
\[ z \cdot w = 1 \]
For our case, we need to find \(w\) such that:
\[ (-16 + 0i) \cdot w = 1 \]

3. **Expressing the Inverse**:
The multiplicative inverse can be expressed as:
\[ w = \frac{1}{-16 + 0i} \]
This simplifies to:
\[ w = \frac{1}{-16} \]

4. **Final Result**:
Therefore, the multiplicative inverse of \(-16\) is:
\[ w = -\frac{1}{16} \]

### Conclusion:
The multiplicative inverse of the complex number \(-16\) is \(-\frac{1}{16}\).