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JEE Advanced Mathematics question

MathematicsComplex NumbersJEE Advanced

If , where is a nonreal complex cube root of unity, are two vertices of an equilateral triangle in the Argand plane then the third vertex may be represented by

Answer: (C)

Solution

, ; they are symmetric about the real axis, with side . So the third vertex lies on the real axis; let it be :

|x - ω|^2 = |

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Question ID VK-110383