Let z be a complex number such that the imaginary part of z is nonzero and a = z^2 + z + 1 is real. Then a **cannot** take the value

JEE Advanced 2012 Mathematics question

Let z be a complex number such that the imaginary part of z is nonzero and is real. Then a **cannot** take the value

Answer: (D)

z satisfies the real quadratic . Since z is not real, this quadratic must have non-real roots: discriminant $1 - 4(1 - a) < 0 ⇒ 4a - 3 < 0 ⇒ a <

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Question ID VK-026048