If \( \operatorname{Re}(z) \) is a positive integer, then value of ...

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If \( \operatorname{Re}(z) \) is a positive integer, then value of the
\( \mathrm{P} \) \( \left|1+z+\ldots+z^{n}\right| \) cannot be less than
(a) \( |z|^{n}-\frac{1}{|z|} \)
(b) \( |z|^{n}+\frac{1}{|z|} \)
(c) \( n|z|^{n} \)
(d) \( n|z|^{n}+1 \)
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