Let C be the set of complex number and `z_(1), z_(2)` are in C.
I. are`(z_(1)) `= arg `(z_(2) )rArr z_(1) = z_(2)`
II. `|z_(1)| = | z_(2) | rArr z_(1) = z_(2)`
Which of the statements given above is `//` are correct ?

Options

A. Only I
B. Only II
C. Both I and II
D. Neither I nor II

Answer

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

### Step-by-Step Solution:

1. **Understanding the First Statement:**
The first statement is:
\[ \text{If } \text{arg}(z_1) = \text{arg}(z_2) \Rightarrow z_1 = z_2 \]
- The argument of a complex number represents the angle it makes with the positive x-axis in the complex plane.
- If two complex numbers have the same argument, they lie on the same line through the origin but may have different magnitudes (moduli).
- Therefore, having the same argument does not guarantee that \( z_1 \) and \( z_2 \) are equal, as they could be different points on the same line.

**Conclusion for Statement I:**
The statement is **false**.

2. **Understanding the Second Statement:**
The second statement is:
\[ |z_1| = |z_2| \Rightarrow z_1 = z_2 \]
- The modulus of a complex number represents its distance from the origin in the complex plane.
- If two complex numbers have the same modulus, they could still have different arguments, meaning they could be located at different points on the circle of radius equal to the modulus.
- Thus, having the same modulus does not imply that \( z_1 \) and \( z_2 \) are equal.

**Conclusion for Statement II:**
The statement is **false**.

### Final Conclusion:
Both statements are incorrect. Therefore, the answer is that neither statement I nor statement II is correct.