Let S_1,S_2,S_3 be S_1=z C:|z-1|√2, S_2=z C:Re[(1-i)z]1, S_3=z C:Im(z)1.

Question

Let $S_1,S_2,S_3$ be $S_1=\{z\in\mathbb C:|z-1|\le\sqrt2\}$, $S_2=\{z\in\mathbb C:\operatorname{Re}[(1-i)z]\ge1\}$, $S_3=\{z\in\mathbb C:\operatorname{Im}(z)\le1\}$. Then the set $S_1\cap S_2\cap S_3$

Accepted Answer

$S_1$ is a disk of radius $\sqrt2$ about $(1,0)$; $S_2$ is the half-plane $x+y\ge1$; $S_3$ is the half-plane $y\le1$. Sketching these three regions shows they overlap in a two-dimensional region, so $S_1\cap S_2\cap S_3$ has infinitely many elements.

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