Sketch the following $$ z\in \mathbb{C}:0 < arg(z-(1+i)) < \frac\pi3 $$ I have considered this geometrically and ended up thinking that the complex numbers $z$ must satisfy $$0 < \frac{Im(z-(1+i))}{Re(z-(1+i))} < \sqrt{3}$$ But this doesn't seem to help. I am thinking im approaching the problem in the wrong way. What is the best way to attempt to sketch this region of $\mathbb{C}$ this without using a computer? Thanks
2026-03-26 09:17:58.1774516678
Sketch $ z\in \mathbb{C}:0 < arg(z-(1+i)) < \frac\pi3 $
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here is a way to plot the region. think of the point $1+i$ as the origin. draw two half rays originating at $1+i$ and one going parallel to the $x$-axis and in the positive direction and the other one at an angle $60^\circ.$ the wedge between the rays is the region you are after.