The area of the region in the Argand plane, in which z satisfies the inequalities 1≤|z−1|≤4 and z+¯¯¯z≥2, is
A
15π
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B
152π
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C
π
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D
None of the above
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Solution
The correct option is B152π Circle 1: |z−1|=1 Circle 2: |z−1|=4 Also Re(z)≥1 From the figure: Area of region A=12×[(Area of circle 1)-(Area of circle 2)] A=π(42−122)=15π2 Hence, option B is corret.