If |z1|=1,|z2|=2,|z3|=3,a n d|9z1z2+4z1z...

If `|z_1|=1,|z_2|=2,|z_3|=3,a n d|9z_1z_2+4z_1z_3+z_2z_3+3|=12 ,` then find the value of `|z_1+z_2+z+3|dot`

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`|z_(1)|=1impliesz_(1)bar(z)_(1)=1,|z_(2)|=2impliesz_(2)bar(z)_(2)=4,|z_(3)|=3impliesz_(3)bar(z)_(3)=9`
Also, `|9z_(1)z_(2)+4z_(1)z_(3)+z_(2)z_(3)|=12`
or `|z_(1)z_(2)z_(3)bar(z)_(3)+z_(1)z_(2)z_(3)bar(z)_(2)+z_(1)bar(z)_(1)z_(2)z_(3)|=12`
or `|z_(1)z_(2)z_(3)||bar(z)_(1)+bar(z)_(2)+bar(z)_(3)|=12`
or `|z_(1)||z_(2)||z_(3)||bar(z)_(1)+bar(z)_(2)+bar(z)_(3)|=12`
or `6|bar(z)_(1)+bar(z)_(2)+bar(z)_(3)|=12`
or `|bar(z)_(1)+bar(z)_(2)+bar(z)_(3)|=2`
or `|z_(1)+z_(2)+z_(3)|=2`

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