Write the additive inverse of the complex numbers. `(-6,5)+(10,-4)`

Answer

To find the additive inverse of the complex numbers given in the question, we will follow these steps:

### Step 1: Identify the complex numbers
The complex numbers given are:
- \( z_1 = (-6, 5) \) which can be written as \( z_1 = -6 + 5i \)
- \( z_2 = (10, -4) \) which can be written as \( z_2 = 10 - 4i \)

### Step 2: Add the complex numbers
Now, we will add the two complex numbers:
\[ z = z_1 + z_2 = (-6 + 5i) + (10 - 4i) \]
Combine the real parts and the imaginary parts:
\[ z = (-6 + 10) + (5i - 4i) = 4 + i \]

### Step 3: Find the additive inverse
The additive inverse of a complex number \( z \) is defined as \( -z \). Therefore, we need to calculate:
\[ -z = -(4 + i) = -4 - i \]

### Final Answer
The additive inverse of the complex number \( (-6, 5) + (10, -4) \) is:
\[ \boxed{-4 - i} \]

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