Let |zi|=i,i=1,2,3,4 and |16 z1z2z3+9z1...

Let `|z_i|=i,i=1,2,3,4` and `|16 z_1z_2z_3+9z_1z_2z_4+4z_1z_3z_4+z_2z_3z_4|=48`, then the value of `|1/barz_1+4/bar z_2+9/bar z_3+16/bar z_4|`

A

1

B

2

C

4

D

8

Text Solution

Verified by Experts

The correct Answer is:

B

We have,
`|16z_(1)z_(2)z_(3)+9z_(1)z_(2)z_(4)+4z_(1)z_(3)z_(4)+z_(2)z_(3)z_(4)|=48`
`rArr |z_(1)z_(2)z_(3)z_(4)||16/z_(4)+9/z_(3)+4/z_(2)+1/z_(1)|=48`
`rArr |z_(1)||z_(2)||z_(3)||z_(4)||(16/z_(4)+9/z_(3)+4/z_(2)+1/z_(1))=48`
`rArr |1/z_(1)+4/z_(2)+9/z_(3)+16/z_(4)|=2`
`rArr |1/z_(1)+4/z_(2)+9/z_(3)+16/z_(4)|=2`

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