JEE (Advanced) 2008 Paper-1

Instructions

Let A, B, C be three sets of complex numbersas defined below
$$A = \left\{z : Imz \geq 1\right\}$$
$$B = \left\{z : \mid z - 2 - i \mid = 3\right\}$$
$$C = \left\{z : Re((1 - i)z) = \sqrt{2}\right\}$$

Question 23

Let z be any point in $$A \bigcap B \bigcap C$$ and let w be any point satisfying $$\mid w - 2 - i \mid < 3$$. Then, $$\mid z \mid - \mid w \mid + 3$$ lies between


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