Let z = 1+ai, be a complex number, a > 0, such that z^3 is a real number. Then the sum 1+z+z^2+ +z^ 11 is equal to :

JEE Main 2016 Mathematics question

Let , be a complex number, , such that is a real number. Then the sum is equal to :

Answer: (2)

Expand . For this to be real the imaginary part must vanish: , and since we get . So , with modulus 2 and argument

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Question ID VK-115645