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JEE Math Practice Question

Let z = 1 + ai be a complex number, a > 0, such that z3 is a real number. Then the sum 1 + z + z2 + . . . . .+ z11 is equal to :

  1. A.$$ - 1250\,\sqrt 3 \,i$$
  2. B.$$ 1250\,\sqrt 3 \,i$$
  3. C.$$1365\,\sqrt 3 i$$
  4. D.$$-$$ $$1365\,\sqrt 3 i$$

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