Yet another question 6

Algebra Level 5

\[ \large \displaystyle \sum_{n=1}^{6a} \log_2 \Bigl(\left \vert f \bigl((1+\sqrt3 i)^n\bigr)\right \vert \Bigr)\]

Let \( f(z) \) be the real part of the complex number \(z\).

Evaluate the summation above for \(a \in \mathbb{Z^+} \).


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