If `|z-4/z|=2`, then the maximum value of`|Z|`is equal to(1) `sqrt(3)+""1`(2) `sqrt(5)+""1`(3) 2(4) `2""+sqrt(2)`A. `1+sqrt(3)`B. `1+sqrt(5)`C. `1-sqrt(5)`D. `sqrt(5)-1`

If `|z-4/z|=2`, then the maximum value of`|Z|`is equal to(1) `sqrt(3)+

1.	If `\|z-4/z\|=2`, then the maximum value of`\|Z\|`is equal to(1) `sqrt(3)+""1`(2) `sqrt(5)+""1`(3) 2(4) `2""+sqrt(2)`A. `1+sqrt(3)`B. `1+sqrt(5)`C. `1-sqrt(5)`D. `sqrt(5)-1`
Answer» Correct Answer - B `\|z-(4)/(z)\|=2` We know `\|a-b\|ge\|a\|-\|b\|` ` therefore \|z-(4)/(z)\|ge\|z\|-\|(4)/(z)\|` `rArr 2 ge \|z\|-(4)/(\|z\|)rArr\|z\|^(2)-2\|z\|-4 le 0` `rArr \|z\|=(2+-sqrt(4-4(1)(-4)))/(2(1))=(2+-sqrt(20))/(2)=(2+-2sqrt(5))/(2)=1+-sqrt(5)` So, `z = 1 + sqrt(5)`.

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