If ` z = 3 -2i` then the value s of ` (Rez)` ` (Im z)^(2)` is

Options

A. 6
B. 12
C. `-6`
D. `-12`

Answer

To solve the problem, we need to find the value of \( (Re(z)) \cdot (Im(z))^2 \) where \( z = 3 - 2i \).

### Step-by-step solution:

1. **Identify the real part of \( z \)**:
- The real part \( Re(z) \) of the complex number \( z = 3 - 2i \) is \( 3 \).

2. **Identify the imaginary part of \( z \)**:
- The imaginary part \( Im(z) \) of the complex number \( z = 3 - 2i \) is \( -2 \).

3. **Calculate the square of the imaginary part**:
- We need to calculate \( (Im(z))^2 \):
\[ (Im(z))^2 = (-2)^2 = 4 \]

4. **Multiply the real part by the square of the imaginary part**:
- Now, we multiply \( Re(z) \) by \( (Im(z))^2 \):
\[ (Re(z)) \cdot (Im(z))^2 = 3 \cdot 4 = 12 \]

5. **Conclusion**:
- The value of \( (Re(z)) \cdot (Im(z))^2 \) is \( 12 \).

### Final Answer:
The value of \( (Re(z)) \cdot (Im(z))^2 \) is \( 12 \).

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