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If |z| < sqrt(2)-1,t h e n|z^2+2zcosalph...

If `|z| < sqrt(2)-1,t h e n|z^2+2zcosalpha|i s` a. less than 1 b. `sqrt(2)+1` c.`sqrt(2)-1` d. none of these

A

less than 1

B

`sqrt(2)+1`

C

`sqrt(2-1)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`|z^(2)+2zcosalpha|le|z^(2)|+|2z cos alpha|`
`=|z|^(2)+2|z||cosalpha|`
`le|z|^(2)+2|z|" "(therefore |cos alpha|le1)`
`lt (sqrt(2)-1)^(2)+2(sqrt(2)-1)=1`
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