Give an example to slow that the substraction of complex numbers is not commutative.

Answer

To show that the subtraction of complex numbers is not commutative, we can follow these steps:

### Step-by-Step Solution:

1. **Define Complex Numbers**:
Let \( z_1 = 2 + 3i \) and \( z_2 = 3 + 4i \), where \( i \) is the imaginary unit.

2. **Calculate \( z_1 - z_2 \)**:
\[ z_1 - z_2 = (2 + 3i) - (3 + 4i) \]
Simplifying this, we get:
\[ z_1 - z_2 = 2 - 3 + 3i - 4i = -1 - i \]

3. **Calculate \( z_2 - z_1 \)**:
\[ z_2 - z_1 = (3 + 4i) - (2 + 3i) \]
Simplifying this, we get:
\[ z_2 - z_1 = 3 - 2 + 4i - 3i = 1 + i \]

4. **Compare the Results**:
We found:
- \( z_1 - z_2 = -1 - i \) (let's call this \( c_1 \))
- \( z_2 - z_1 = 1 + i \) (let's call this \( c_2 \))

Now we compare \( c_1 \) and \( c_2 \):
\[ c_1 = -1 - i \quad \text{and} \quad c_2 = 1 + i \]
Clearly, \( c_1 \neq c_2 \).

5. **Conclusion**:
Since \( z_1 - z_2 \neq z_2 - z_1 \), we conclude that subtraction of complex numbers is not commutative.