If z(1),z(2),z(3) represent the vertices...

If `z_(1),z_(2),z_(3)` represent the vertices of an equilateral triangle such that `|z_(1)|=|z_(2)|=|z_(3)|`, then

`z_(1)+z_(2)=z_(3)`

`z_(1)+z_(2)+z_(3)=0`

`z_(1) z_(2)=(1)/(z_(3))`

`z_(1)-z_(2)=z_(3)-z_(2)`

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