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If y(1)=max||z-omega|-|z-omega^(2)||, wh...

If `y_(1)=max||z-omega|-|z-omega^(2)||`, where `|z|=2` and `y_(2)=max||z-omega|-|z-omega^(2)||`, where `|z|=(1)/(2)` and `omega` and `omega^(2)` are complex cube roots of unity, then

A

`y_(1)=sqrt(3)`, `y_(2)=sqrt(3)`

B

`y_(1) lt sqrt(3)`, `y_(2)=sqrt(3)`

C

`y_(1)=sqrt(3)`, `y_(2) lt sqrt(3)`

D

`y_(1) gt 3`, `y_(2) lt sqrt(3)`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` We have `||z_(1)|-|z_(2)|| le |z_(1)-z_(2)|` and equality holds only when `argz_(1)=argz_(2)`
`implies||z-w|-|z-w^(2)|| le |w^(2)-w| le sqrt(3)` and equality canhold only when `|z|=2` and not when `|z|=(1)/(2)`
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