Let  be three sets$S_1,S_{2}and{S}_3$ defined as 

          $\begin{array}{l}{S}_1=\left\{x\in C:\left|z-1\right|\le \sqrt{2}\right\}\\ S_2=\left\{z\in C:\mathrm{Re}\left(\left(1-i\right)z\right)\ge 1\right\}\\ S_3=\left\{z\in C:lm\left(z\right)\le 1\right\}\end{array}$

          Then the set $S_1\cap S_2\cap S_3$

The given sets are 

$\begin{array}{c}{S}_1:{\left(x-1\right)}^2+y^2\le 2\\ S_2:x+y\ge 1\\ S_3:y\le 1\end{array}$

The graph shows the common region to the above three regions 

Therefore, the common region to three regions is infinite