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If |z-4/z|=2 , then the maximum value of...

If `|z-4/z|=2` , then the maximum value of `|Z|` is equal to (1) `sqrt(3)+""1` (2) `sqrt(5)+""1` (3) 2 (4) `2""+sqrt(2)`

A

`sqrt(5)`

B

`sqrt(5)+1`

C

`sqrt(5)-1`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
`|z|=|z-4/z+4/z| le |z-4/z|+|4/z|` [By triangle inequlity]
`rArr |z| le 2 +4/|z|` `[therefore |z-4/z|=2]`
`rArr |z|^(2)-2|z|-4 le0`
`rArr (|z|-1+sqrt(5)) le 0`
`rArr 1-sqrt(5) le |z| le 1 + sqrt(5)`
Thus, the maximum value of `|z|` is `1+sqrt(5)`.
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