If `z_1,z_2, z_3` are complex numbers such that `|z_1|=|z_2|=|z_3|=|1/z_1+1/z_2+1/z_3|=1` then `|z_1+z_2+z_3|` is equal to

Options

A. equal to 1
B. less than 1
C. greater than 1
D. equal to 3

Answer

A

Explanation

We have,
`|z_(1)|=|z_(2)|=|z_(3)|=1`
`rArr |z_(1)|^(2)=|z_(2)|^(2)=|z_(3)|^(2)=1`
`rArr z_(1)barz_(1)=z_(2)barz_(2)=z_(3)barz_(3)=1 rArr 1/z_(1)=barz_(1),1/z_(2),1/z_(2)=barz_(2), 1/z_(3)=barz_(3)`
Now, `|1/z_(1)+1/z_(2)+1/z_(3)|=1`
`rArr |barz_(1)+barz_(2)+barz_(3)|=1 rArr |bar(z_(1)+z_(2)+z_(3))|=1 rArr |z_(1)+z_(2)+z_(3)|=1`