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If |z^2-3|=3|z| , then the maximum value...

If `|z^2-3|=3|z|` , then the maximum value of `|z|` is `1` b. `(3+sqrt(21))/2` c. `(sqrt(21)-3)/2` d. none of these

A

1

B

`(3+sqrt(21))/(2)`

C

`(sqrt(21) -3)/(2)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`|z^(2)-3|ge|z|^(2)-3`
`rArr 3|z|ge|z|^(2)-3`
`rArr |z|^(2)-3|z|-3le0`
`rArr 0lt|z|le(3+sqrt(21))/(2)`
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