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

  • A
    $-1$
  • B
    $\frac{1}{3}$
  • C
    $\frac{1}{2}$
  • D
    $\frac{3}{4}$

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