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The maximum value of |z| where z satisfi...

The maximum value of |z| where z satisfies the condition` |z+(2/z)|=2` is

A

`sqrt(3)-1`

B

`sqrt(3)`

C

`sqrt(3)+1`

D

`sqrt(2)+sqrt(3)`

Text Solution

Verified by Experts

The correct Answer is:
C
We have,
`|z|=|z+2/z-2/z|`
`rArr |z| le |z+2/z+-2/z|`
`|z| le |z+2/z|+|-2/z|` [Using triangle inequality]
`rArr |z| le 2 + 2/|z|` `[therefore |z+2/z|=2]` (given)
`rArr |z|^(2)-2|z|-2 le 0`
`rArr {|z|-1+sqrt(3)}{|z|-1-sqrt(3)} le 0`
`rArr 1-sqrt(3) le |z| le 1+sqrt(3)`
Thus, the maximum value of `|z|` is `1+sqrt(3)`.
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