[AzMa1]

So I was checking a math problem recently: ln((2-√4+4)/2), and to my surprise, the answer came out to be -0.881373587 + 3.141592654i. How did pi work its way in there? Of course it turned out that
ln((x-√(x^2 +4))/2) alway produced a πi in the answer. Now I'm a newbie at this stuff so there might be an easy explanation for this but I can't seem to find one. Does someone know why this happens?

[Yggdrasil]

It probably has to do with the fact that

e^iπ = -1

or in logarithm form

ln(-1) = iπ

For more on why this is see: http://en.wikipedia.org/wiki/Euler%27s_identity

[Martingale]

it actually has many values 

http://en.wikipedia.org/wiki/Complex_logarithm#Log.28z.29_as_a_multi-valued_function


(2-sqrt(4+4))/2=1-sqrt(2)

ln(1-sqrt(2))=ln(sqrt(2)-1)+PI*i   


so e^(ln(sqrt(2)-1)+PI*i )=1-sqrt(2)

also

e^(ln(sqrt(2)-1)+3*PI*i)=1-sqrt(2)

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