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If log sqrt(3)((|z|^(2)-|z|+1)/(2+|z|))g...

If log `sqrt(3)((|z|^(2)-|z|+1)/(2+|z|))gt2`, then the locus of z is

A

`|z|gt 1`

B

`|z|lt5`

C

`|z|gt 5`

D

`|z|lt 1`

Text Solution

Verified by Experts

The correct Answer is:
C
We have log `sqrt(3)((|z|^(2)-|z|+1)/(2+|z|))gt 2`
`rArr (|z|^(2)-|z|+1)/(2+|z|)gt(sqrt(3))^(2)`
`rArr|z|^(2)-4|z|-5 gt 0`
`rArr (|z|+1)(|z|-5)gt0`
`rArr|z|-5gt0`
`rArr |z|gt 5`
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