Area of triangle formed by the vertices `z, omega z and z+omega z` is – InterviewSolution

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1.	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)`
Answer» `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` `z, z omega , - z omega^2 ` area = `\|z\|^2 xx sqrt3/4 = 4/sqrt3` `\|z\|^2 = 16/3` `\|z\| = 4/ sqrt3` Answer

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