Let \( A, B \) and \( C \) be three sets of complex numbers as defi... VIDEO
Let \( A, B \) and \( C \) be three sets of complex numbers as defined below:
\[
\begin{array}{l}
A=\{z: \operatorname{Im}(z) \geq 1\} \\
B=\{z:|z-2-i|=3\} \\
C=\{z: \operatorname{Re}((1-i) z)=\sqrt{2}\}, \text { where } i=\sqrt{-1}
\end{array}
\]
\( \mathrm{P} \)
[IIT-JEE 2008, 4+4+4M]
The number of elements in the set \( A \cap B \cap C \), is
(a) 0
(b) 1
(c) 2
(d) \( \infty \)
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