If `|z_1|=2,|z_2|=3,|z_3|=4` and `|2z_1+3z_2+4z_3|=4` then the expression `|8z_2z_3+27z_3z_1+64z_1z_2|` equals

Options

A. 24
B. 48
C. 72
D. 96

Answer

D

Explanation

We have,
`|8z_(2)z_(3)+27z_(3)z_(1)+64z_(1)z_(2)|`
`=|z_(1)z_(2)z_(3)(8/z_(1)+27/z_(2)+64/z_(3))|`
`=|z_(1)||z_(2)||z_(3)||(8barz_(1))/|z_(1)|^(2) + (27barz_(2))/(|z_(2)|^(2)) + (64barz_(3))/(|z_(3)|^(2))|`
`=24|2barz_(1)+3barz_(2)+4barz_(3)|`
`=24|bar(2z_(1)+3z_(2)+4z_(3))|`
`=24|2z_(1)+3z_(2)+4z_(3)|=24 xx 4 =96`