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 $\text{arg}(\overline{z}) = -\theta$.

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!