1.

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

Answer»

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

SOLUTION :`(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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