Let C1 and C2 are concentric circles of radius 1 unit and 8/3 unit , respectively, having centre at (3,0) on the Argand plane. If the complex number z satisfies the inequality log1/3(|z−3|2+211|z−3|−2)>1 then
A
z lies outside C1 but inside C2
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B
z lies inside C1
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C
z lies outside C2
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D
none of these
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Solution
The correct option is Az lies outside C1 but inside C2 log1/3(|z−3|2+211|z−3|−2)>1
Let |z−3|=t⇒t>0
for function to be defined t2+211t−2>0 ⇒t>211⋯(1)