InterviewSolution
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InterviewSolution
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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, thenA. `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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Answer» 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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