Let S1, S2 and S3 be three sets defined as S1 = {z ∈ C : |z - 1| ≤ √2}

Question

Let S₁, S₂ and S₃ 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

Answer 1

Answer is (3)

For |z - 1| \(\leq \sqrt{2},\) z lies on and inside the circle of radius \(\sqrt{2}\) units and centre (1, 0).

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