Let \( z \) be a complex number such that the imaginary part of \( ...

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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
\( \mathrm{P} \) take the value
[IIT-JEE 2012, 3M]
W
(a) \( -1 \)
(b) \( \frac{1}{3} \)
(c) \( \frac{1}{2} \)
(d) \( \frac{3}{4} \)
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