1. arg(z)=\frac{\pi}{4}

Describe the set of points z in the complex plane that satisfy $\displaystyle arg(z)=\frac{\pi}{4}$.

Is this question just asking for $\displaystyle x=\frac{\sqrt{2}}{2}$ and $\displaystyle y=\frac{\sqrt{2}}{2}$?

2. no, the set is a whole line, not just one point. All complex numbers on the line $\displaystyle r(\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}\cdot i)=r e^{i \frac{\pi}{4}}$ for r $\displaystyle \in \mathbb{R}, r>0$.
Describe the set of points z in the complex plane that satisfy $\displaystyle arg(z)=\frac{\pi}{4}$.
Is this question just asking for $\displaystyle x=\frac{\sqrt{2}}{2}$ and $\displaystyle y=\frac{\sqrt{2}}{2}$?
4. Which means it is the set $\displaystyle \{a+ bi| a= b, a> 0\}$