Let $S_1, S_2$ and $S_3$ be three sets defined as
$$
\begin{aligned}
& S_1=\{z \in \mathbb{C}:|z-1| \leq \sqrt{2}\} \\
& S_2=\{z \in \mathbb{C}: \operatorname{Re}((1-i) z) \geq 1\} \\
& S_3=\{z \in \mathbb{C}: \operatorname{Im}((z) \leq 1\}
\end{aligned}
$$
Then the set $\mathrm{S}_1 \cap \mathrm{~S}_2 \cap \mathrm{~S}_3$
