InterviewSolution
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InterviewSolution
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If `|z_(1)|=|z_(2)|=|z_(3)|=1 and z_1+z_2+z_3=0`then the area of the triangle whose vertices are `z_1, z_2, z_3`isA. `3sqrt(3//4)`B. `sqrt(3//4)`C. 1D. 2 |
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Answer» Correct Answer - A `|z_(1)|=|z_(2)|=|z_(3)|=1` Hence, the cirumcenter of triangle is origin. Also, centroid `(z_(1)+z_(2)+z_(3))//3=0`, which coincides with the circumcentrer. So the triangle is equilateral . Since radius is 1, length of side is `a=sqrt(3)`. Therefore, the area of the triangle is `(sqrt3//4)a^(2)=(3sqrt3//4)`. |
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