Complex Numbers $- \arg(-z)$

Question

$$\operatorname{Arg}(-z)=\frac{3\pi}4$$

$$\operatorname{Arg}(-z) - \operatorname{Arg} (z) = \pm \pi$$

$$\implies \operatorname{Arg}(z) = \frac{3\pi}4 + \pi = \frac{7\pi}4$$

so, the solution is a line in the complex plane at $315^\circ$.

Am I doing it right?

Answer 1

Notice that $\operatorname{Arg}(z) \in (-\pi, \pi]$, hence $$\operatorname{Arg}(z) = \frac{7\pi}{4}-2\pi=-\frac{\pi}4$$

It is a half line/ray in the complex plane at $315$ degrees.

Answer 2

More precisely the solution is a ray in the complex plane at 315 degrees.