This might get fixed in the future, but at the time of this writing, Wolfram Alpha gets apparently sometimes confused by logarithms of complex numbers:
Wolfram Alpha -- $\log(1+ \frac{1}{2}i) - \log(1 - \frac{1}{2} i)$
For reference, should the problem get fixed: it claims that $2i = 2i\cot^{-1}(2) \approx 0.9272$.
Curiously, the numerical approximation is correct, but the symbolic form seems to be wrong.
