Let \( \mathrm{A}, \mathrm{B}, \mathrm{C} \) be three sets of complex numbers as defined below.
\( \mathrm{P} \)
\( \mathrm{A}=\{\mathrm{z}:|\mathrm{z}+1| \leq 2+\operatorname{Re}(\mathrm{z})\}, \quad \mathrm{B}=\{\mathrm{z}:|\mathrm{z}-1| \geq 1\} \) and \( \mathrm{C}=\left\{\mathrm{z}:\left|\frac{\mathrm{z}-1}{\mathrm{z}+1}\right| \geq 1\right\} \)
The real part of the complex number in the region \( \mathrm{A} \cap \mathrm{B} \cap \mathrm{C} \) and having maximum amplitude is
(A) \( -1 \)
(B) \( \frac{-3}{2} \)
(C) \( \frac{1}{2} \)
(D) \( -2 \)
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