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Question

The locus of the complex number z in an argand plane satisfying the inequality log1/2(|z1|+43|z1|2)>1( where |z1|23) is

A
A circle
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B
Interior of a circle
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C
Exterior of a circle
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D
None of these
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Solution

The correct option is D Exterior of a circle
We have, log1/2(|z1|+43|z1|2)>1=log1/2(12)
|z1|+43|z1|2<12<1
(logax is a decreasing function if a<1)
|z1|+4<3|z1|22|z1|>6|z1|>3
which is exterior of a circle

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