Find the multiplicative inverse of each of the following complex numbers when it exists.
`0+0i`

Answer

To find the multiplicative inverse of the complex number \(0 + 0i\), we can follow these steps:

### Step 1: Understand the concept of multiplicative inverse
The multiplicative inverse of a complex number \(z\) is defined as \(\frac{1}{z}\). For a complex number to have a multiplicative inverse, \(z\) must not be equal to zero.

### Step 2: Identify the given complex number
The complex number given in the question is \(0 + 0i\), which is simply \(0\).

### Step 3: Calculate the multiplicative inverse
To find the multiplicative inverse of \(0 + 0i\), we would compute:
\[ \text{Multiplicative Inverse} = \frac{1}{0 + 0i} = \frac{1}{0} \]

### Step 4: Analyze the result
The expression \(\frac{1}{0}\) is undefined in mathematics. Therefore, the multiplicative inverse of \(0 + 0i\) does not exist.

### Conclusion
The multiplicative inverse of the complex number \(0 + 0i\) does not exist.

---