Let S_{1}, S_{2} and S_{3} be three sets defined as

\(S_1=\{z \in \mathbb C:|z-1|\leq \sqrt{2}\}\)

\(S_2=\{z \in \mathbb C:\text{Re} \big((1-i)z\big)\geq 1\}\)

\(S_3=\{z \in \mathbb C:\text{Im}(z)\leq 1\}\)

Then the set \(S_1\cap S_2\cap S_3\)

**(1)** Is a singleton

**(2)** Has exactly two elements

**(3)** Has infinitely many elements

**(4)** Has exactly three elements