99 Percentile Qs Bank for JEE MainMathematicsComplex Number

If _ 1 3 |z|^2-|z|+1 2+|z| >-2 , then z lies inside

Options

Aa triangle
Ban ellipse
Ca circle
Da square

Correct answer

C. a circle

Step-by-step solution

Given that, _ 1 3 |z|^2-|z|+1 2+|z| >-2 Since, _a b>c, b < a^c if 0 < a < 1 aligned & |z|^2-|z|+1 2+|z| < ( 1 3 )⁻² & |z|^2-|z|+1 2+|z| < ( 3 )^2 aligned aligned & |z|^2-|z|+1 < ( 3 )^2(2+|z|) & |z|^2-|z|+1 < 6+3|z| & |z|^2-4|z|+1 < 6 & (|z|-2)^2 < 9 -3 < |z|-2 < 3 & -1 < |z| < 5 0 < |z| < 5 aligned Hence, z lies inside the circle.

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