What is the additive inverse of `-2+3i`.

Answer

To find the additive inverse of the complex number \(-2 + 3i\), we follow these steps:

### Step 1: Understand the Concept of Additive Inverse
The additive inverse of a number \(z_1\) is another number \(z_2\) such that when you add them together, the result is zero. Mathematically, this can be expressed as:
\[ z_1 + z_2 = 0 \]

### Step 2: Identify the Given Complex Number
Here, the complex number is:
\[ z_1 = -2 + 3i \]

### Step 3: Set Up the Equation
To find the additive inverse \(z_2\), we need to find a complex number such that:
\[ (-2 + 3i) + z_2 = 0 \]

### Step 4: Solve for the Additive Inverse
To isolate \(z_2\), we can rearrange the equation:
\[ z_2 = -(-2 + 3i) \]
This simplifies to:
\[ z_2 = 2 - 3i \]

### Step 5: Conclusion
Thus, the additive inverse of the complex number \(-2 + 3i\) is:
\[ \boxed{2 - 3i} \]

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