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The question of concern is the following. Sketch the subset $S$ where $S={z: \frac{-\pi}{4}\le Arg(z-(-2+i)) \le \frac{3\pi}{4}} $. The provided answer is the following.

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This is where I am confused. Why is there a dotted boundary line here? Would the sketch not be equivalent to first sketching $\frac{-\pi}{4} \le Arg(z)\le \frac{3\pi}{4}$ which would not have such boundary line, and then translating the origin up to the point $-2+i$. Thank you in advance.

Swiss Gnome
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    This looks like it's missing some other conditions. Going by just what's provided, there is no reason why the shaded area would stop at the imaginary axis, either. – dxiv Mar 12 '22 at 08:25
  • Interesting. The question I have provided is the exact same as the one asked in the textbook. – Swiss Gnome Mar 12 '22 at 08:27

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