Give an example to show that subtraction of complex number is not commutative.

Answer

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

### Step 1: Define two complex numbers
Let \( Z_1 = 2 + 3i \) and \( Z_2 = 3 + 4i \).

### Step 2: Perform the subtraction \( Z_1 - Z_2 \)
We calculate:
\[ Z_1 - Z_2 = (2 + 3i) - (3 + 4i) \]
Subtract the real parts and the imaginary parts:
\[ = (2 - 3) + (3i - 4i) = -1 - i \]

### Step 3: Perform the subtraction \( Z_2 - Z_1 \)
Now, we calculate:
\[ Z_2 - Z_1 = (3 + 4i) - (2 + 3i) \]
Again, subtract the real parts and the imaginary parts:
\[ = (3 - 2) + (4i - 3i) = 1 + i \]

### Step 4: Compare the results
From the calculations:
- \( Z_1 - Z_2 = -1 - i \)
- \( Z_2 - Z_1 = 1 + i \)

Since \( -1 - i \neq 1 + i \), we can conclude that:
\[ Z_1 - Z_2 \neq Z_2 - Z_1 \]

### Conclusion
Therefore, the subtraction of complex numbers is not commutative.

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