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 c

Monjur Alahi

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)`


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Salim Ahmed Kawsar

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Correct Answer - 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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