Write the additive inverse of the complex numbers.
`(2,1)(-4,6)`

Answer

To find the additive inverse of the given complex numbers \( Z_1 = 2 + i \) and \( Z_2 = -4 + 6i \), we can follow these steps:

### Step 1: Identify the complex numbers
The complex numbers given are:
- \( Z_1 = 2 + i \)
- \( Z_2 = -4 + 6i \)

### Step 2: Understand the concept of additive inverse
The additive inverse of a complex number \( Z \) is another complex number \( Z' \) such that:
\[ Z + Z' = 0 \]
This means that \( Z' = -Z \).

### Step 3: Find the additive inverse of \( Z_1 \)
To find the additive inverse of \( Z_1 \):
\[ Z_1' = -Z_1 = - (2 + i) \]
Calculating this gives:
\[ Z_1' = -2 - i \]

### Step 4: Find the additive inverse of \( Z_2 \)
Now, to find the additive inverse of \( Z_2 \):
\[ Z_2' = -Z_2 = - (-4 + 6i) \]
Calculating this gives:
\[ Z_2' = 4 - 6i \]

### Step 5: Write the final answers
The additive inverses of the given complex numbers are:
- The additive inverse of \( Z_1 \) is \( -2 - i \).
- The additive inverse of \( Z_2 \) is \( 4 - 6i \).

### Summary of the solution:
- Additive inverse of \( Z_1 = 2 + i \) is \( -2 - i \).
- Additive inverse of \( Z_2 = -4 + 6i \) is \( 4 - 6i \).

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