Write the additive inverse of the following
`3- 4i`

Answer

To find the additive inverse of the complex number \(3 - 4i\), we can follow these steps:

### Step 1: Understand the concept of additive inverse
The additive inverse of a number \(Z\) is a number \(Z'\) such that when you add them together, the result is zero. In mathematical terms, this can be expressed as:
\[ Z + Z' = 0 \]

### Step 2: Identify the complex number
In this case, the complex number given is:
\[ Z = 3 - 4i \]

### Step 3: Set up the equation for the additive inverse
Let the additive inverse be \(Z'\). According to the definition, we have:
\[ Z + Z' = 0 \]
Substituting \(Z\) into the equation, we get:
\[ (3 - 4i) + Z' = 0 \]

### Step 4: Solve for the additive inverse
To find \(Z'\), we can rearrange the equation:
\[ Z' = - (3 - 4i) \]
Distributing the negative sign gives:
\[ Z' = -3 + 4i \]

### Step 5: Write the final answer
Thus, the additive inverse of the complex number \(3 - 4i\) is:
\[ -3 + 4i \]

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