Statement-1 : let ` z_(1) and z_(2)` be two complex numbers such that arg `(z_(1)) = pi/3 and arg(z_(2)) = pi/6 " then arg " (z_(1) z_(2)) = pi/2`
and
Statement -2 : ` arg(z_(1)z_(2)) = arg(z_(1)) + arg(z_(2)) + 2kpi, k in { 0,1,-1}`

Options

A. Statement -1 is True, Statement -2 is True, Statement -2 is a correct explanation for statement -1
B. Statement -1 is True, Statement -2 is True , Statement -2 is NOT a correct explanation for Statement -1
C. Statement -1 is True, Statement -2 is False
D. Statement -1 is Flase, Statement -2 is True

Answer

To solve the problem, we need to analyze both statements regarding the complex numbers \( z_1 \) and \( z_2 \).

### Step-by-Step Solution:

1. **Understanding the Arguments**:
Given:
- \( \arg(z_1) = \frac{\pi}{3} \)
- \( \arg(z_2) = \frac{\pi}{6} \)

2. **Using the Property of Arguments**:
The property of the argument of the product of two complex numbers states:
\[ \arg(z_1 z_2) = \arg(z_1) + \arg(z_2) + 2k\pi \quad \text{(where \( k \) is an integer)} \]
Therefore, we can write:
\[ \arg(z_1 z_2) = \frac{\pi}{3} + \frac{\pi}{6} + 2k\pi \]

3. **Finding a Common Denominator**:
To add \( \frac{\pi}{3} \) and \( \frac{\pi}{6} \), we need a common denominator:
\[ \frac{\pi}{3} = \frac{2\pi}{6} \]
Thus,
\[ \arg(z_1 z_2) = \frac{2\pi}{6} + \frac{\pi}{6} + 2k\pi = \frac{3\pi}{6} + 2k\pi = \frac{\pi}{2} + 2k\pi \]

4. **Considering \( k = 0 \)**:
If we set \( k = 0 \):
\[ \arg(z_1 z_2) = \frac{\pi}{2} \]
This shows that the argument of the product \( z_1 z_2 \) is indeed \( \frac{\pi}{2} \).

5. **Conclusion**:
- **Statement 1** is true: \( \arg(z_1 z_2) = \frac{\pi}{2} \).
- **Statement 2** is also true as it correctly describes the relationship between the arguments of the product of two complex numbers.

### Final Answer:
Both statements are true.