If `z_(1)=(2,-1),z_(2)=(6,3)` find `z_(1)-z_(2)`

Answer

To solve the problem of finding \( z_1 - z_2 \) where \( z_1 = (2, -1) \) and \( z_2 = (6, 3) \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Complex Numbers**:
- Given \( z_1 = (2, -1) \), we can express this in standard complex number form:
\[ z_1 = 2 - i \]
- Given \( z_2 = (6, 3) \), we express this as:
\[ z_2 = 6 + 3i \]

2. **Set Up the Subtraction**:
- We need to find \( z_1 - z_2 \):
\[ z_1 - z_2 = (2 - i) - (6 + 3i) \]

3. **Distribute the Negative Sign**:
- Distributing the negative sign gives:
\[ z_1 - z_2 = 2 - i - 6 - 3i \]

4. **Combine Like Terms**:
- Combine the real parts and the imaginary parts:
\[ z_1 - z_2 = (2 - 6) + (-i - 3i) \]
\[ = -4 - 4i \]

5. **Final Result**:
- Therefore, the result of \( z_1 - z_2 \) is:
\[ z_1 - z_2 = -4 - 4i \]

### Summary of the Solution:
The final answer is:
\[ z_1 - z_2 = -4 - 4i \]