This is ridiculous!

Algebra Level pending

If
\(\Gamma(\frac{1}{2}) \cdot ln(i^i)=a \pi^b\)
\( i^{i} \) is multivalued and can be written as \( e^{\ x } \) for multiple values of x. For the question, only consider \( x \in (-\pi, \pi) \)

what is \(a+b\)?

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