How to draw this dark area to $w=\frac{z+1}{z-1}$ so difficult to draw LFT...
2026-03-25 07:40:00.1774424400
how to draw LFT?
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Remember:
The point $1$ goes to $\infty$. This means that the two circles bordering the gray are are transformed in parallel lines (since they touch with the same tangent at $z=1$.) Moreover, these lines must be perpendicular to the image of the real axis, which happens to be the real axis again. The rest should be easy.