How to get from $x<x^2 + y^2$ to $\left(\frac12\right)^2<\left(x-\frac12\right)^2 +y^2$?
This is were I saw it: Sketch all points in the complex plane such that $\mathrm{Re}(1/z)<1$
2026-04-03 07:28:48.1775201328
how to get from $x<x^2 + y^2$ to $\left(\frac12\right)^2<\left(x-\frac12\right)^2 +y^2$?
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Add on both sides $1/4$:
$${1\over 4}<{1\over 4} -x+x^2+y^2$$ so $$ \big({1\over 2}\big)^2<(x-{1\over 2})^2+y^2$$