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If z a complex number satisfying |z^(3)+...

If z a complex number satisfying `|z^(3)+z^(-3)|le2`, then the maximum possible value of `|z+z^(-1)|` is -

A

2

B

`3sqrt(2)`

C

`2sqrt(2)`

D

1

Text Solution

Verified by Experts

The correct Answer is:
A
`|z^(3)+z^(-3)|le2`
`|z^(3)+(1)/(z^(3))|le2`
`|(z+(1)/(z))(z^(2)+(1)/(z^(2)))|le2`
`|(z+(1)/(z))((z+(1)/(z))^(2)-3)|le2`
`|z+(1)/(z)||(z+(1)/(z))^(2)-3|le2`
`|z+(1)/(z)|{|z+(1)/(z)|^(2)-3|}le2" "{because|z^(1)-z_(2)|le||z_(1)|-z^(2)||}`
`t|t^(2)-3|le2" "(tle0)"where t" =|z+(1)/(z)|`
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