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I am trying to calculate $$\log(-1+i)$$

I have $$\log(-1+i) = \ln|(-1+i)| + i\operatorname{Arg}(-1+i)$$

$$ = \ln\sqrt2 + i3\pi/4$$

However when I checked that in matlab and wolfram alpha they have

$$\frac{\ln\sqrt2}{2} + i3\pi/4$$

Can't see what Im doing wrong.

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up vote 5 down vote accepted

In fact Wolfram Alpha returns $\dfrac {\ln 2}2+i\dfrac{3\pi}4$ so that both are equal!

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God damn, I am terrible for overlooking numbers and signs. Its gonna cost me in the exam :( – Jim_CS Apr 18 '12 at 0:44
@jim: fast reading is a common and shared default ;-) – Raymond Manzoni Apr 18 '12 at 6:26

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