If `z_(1),z_(2),z_(3)` are three complex numbers, such that `|z_(1)|=|z_(2)|=|z_(3)|=1` & `z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=0` then `|z_(1)^(3)+z_(2)^(3)+z_(3)^(3)|` is equal to _______. (not equal to 1)

Answer

3

Explanation

`:. z_(1)=zimpliesz_(2)^(2)=z^(2)omega^(2),z_(3)=z_(2)^(2)omega^(2)`
`:. (z_(2))/(z_(1))=+omega` or `-omega`
`(z_(3))/(z_(1))=+omega^(2)` or `-omega^(2)`