If `z_(1)= 4-3i and z_(2) = 3 + 9i " then " z_(1) -z_(2)` is

Options

A. 1+ 12i
B. `-1 +12i`
C. ` 1- 12i`
D. ` -1-12i`

Answer

To solve the problem of finding \( z_1 - z_2 \) where \( z_1 = 4 - 3i \) and \( z_2 = 3 + 9i \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Complex Numbers**:
\[ z_1 = 4 - 3i \]
\[ z_2 = 3 + 9i \]

2. **Set Up the Subtraction**:
We need to calculate \( z_1 - z_2 \):
\[ z_1 - z_2 = (4 - 3i) - (3 + 9i) \]

3. **Distribute the Negative Sign**:
When subtracting \( z_2 \), distribute the negative sign:
\[ z_1 - z_2 = 4 - 3i - 3 - 9i \]

4. **Combine the Real Parts**:
Combine the real parts (the numbers without \( i \)):
\[ 4 - 3 = 1 \]

5. **Combine the Imaginary Parts**:
Combine the imaginary parts (the coefficients of \( i \)):
\[ -3i - 9i = -12i \]

6. **Write the Final Result**:
Now, combine the results from the real and imaginary parts:
\[ z_1 - z_2 = 1 - 12i \]

### Final Answer:
Thus, the result of \( z_1 - z_2 \) is:
\[ \boxed{1 - 12i} \]