A \( \frac{1}{2} log_{e}{2} + \frac{\pi}{4} i \)
B \( 2 log_{e}{2} + \frac{\pi}{4} i \)
C \( \frac{1}{2} log_{e}{2} - \frac{\pi}{4} i \)
D \( \frac{1}{2} log_{e}{2} + \left ( 2 n + \frac{1}{4} \right ) \pi i \)
Correct Answer: Option A
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