if ` z_(1),z_(2),z_(3),…..z_(n)` are complex numbers such that ` |z_(1)|=|z_(2)| =….=|z_(n)| = |1/z_(1) +1/z_(2) + 1/z_(3) +….+1/z_(n)| =1`
Then show that `|z_(1) +z_(2) +z_(3) +……+z_(n)|=1`

Explanation

A complex number z is said to be unimodular iff `|z|=1` and unimodular complex number z can be represented by ` z=e^(itheta) = cos theta + isin theta`
Also, |z|=1
` Rightarrow z barz =1`
` Rightarrow 1/z = barz `
Now,` |1/z_(1) +1/z_(2)+1/z_(3) +.....+1/z_(n)|=1`
`Rightarrow |barz_(1)+barz_(2)+barz_(3)+.....+barz_(n)|=1`
`|bar(z_(1)+z_(2)+z_(3)+......z_(n))|=1`
`Rightarrow |z_(1)+z_(2)+z_(3)+....+z_(n)|=1 ,"as" |z|=|barz|`