Let a be a complex number such that |a|<1 and z_1,z_2, be vertices of a polygon such that z_k=1+a+a^2+ +a^ k-1 . Then the vertices of the polygon lie within a circle

JEE Main Mathematics question

Let be a complex number such that and be vertices of a polygon such that . Then the vertices of the polygon lie within a circle

Answer: (C)

, so . Hence

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Question ID VK-013617