Given \( \mathrm{f}(\mathrm{z})= \) the real part of a complex number \( \mathrm{z} \). For exam...

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Given \( \mathrm{f}(\mathrm{z})= \) the real part of a complex number \( \mathrm{z} \). For example, \( \mathrm{f}(3-4 \mathrm{i})=3 \). If \( \mathrm{a} \in \mathrm{N}, \mathrm{n} \in \mathrm{N} \) then find the value of \( \sum_{n=1}^{6 a} \log _{2}\left|f(1+i \sqrt{3})^{n}\right| \) ?
(a) \( 18 \mathrm{a}^{2}-\mathrm{a} \)
(b) \( 18-\mathrm{a}^{2} \)
(c) \( 18 \mathrm{a}-\mathrm{a}^{2} \)
(d) \( 18 \mathrm{a}^{2}+\mathrm{a} \)
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