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Area of triangle formed by the vertices ...

Area of triangle formed by the vertices `z, omega z and z+omega z` is `4/sqrt(3)`, `omega` is complex cube roots of unity then `|z|` is (A) `1` (B) `4/3` (C) `3/4` (D) `4/(sqrt3)`

Text Solution

Verified by Experts

`1 + omega + omega^2 = 0`
`z, z omega , z + z omega`
`z , z omega , z(1 + omega)`
`z , z omega , - z omega^2 `
area `/_ ABC= 1/2 xx b xxh `
`1/2 xx AB xx OD`
`1/2 xx 1 xx sqrt3/2 = sqrt3/4`
so `1, omega , -omega^2`
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