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The problem states:

**2) If \(\text{arg}(z) = \theta\), then \(\text{arg}(\overline{z}) =\)?**

Here, \(z\) is a complex number, and \(\overline{z}\) denotes its complex conjugate. 

### Solution:
For any complex number \(z = r(\cos\theta + i\sin\theta)\), its argument, denoted as \(\text{arg}(z)\), is \(\theta\). The complex conjugate of \(z\) is \(\overline{z} = r(\cos(-\theta) + i\sin(-\theta))\), where \(\text{arg}(\overline{z}) = -\theta\).

Thus, if \(\text{arg}(z) = \theta\), then \(\text{arg}(\overline{z}) = -\theta\).

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Would you like more details or have any further questions?

Here are five related questions:
1. What is the geometrical meaning of the argument of a complex number?
2. How do you compute the argument for negative complex numbers?
3. How is the magnitude of a complex number affected by its conjugate?
4. Can two different complex numbers have the same argument?
5. How does multiplication affect the arguments of two complex numbers?

**Tip:** When dealing with complex numbers, always remember that the argument of a conjugate complex number flips its sign!

Explore how to find the argument of the conjugate of a complex number when the argument of the original number is given. Learn key concepts of complex numbers and complex conjugates in this problem suitable for Grades 11-12.

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