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Mathematics
OpenStudy (anonymous):

how to prove i^i is a real number?

OpenStudy (anonymous):

Use ln(-1)

OpenStudy (anonymous):

\[i^i\] first write \[i=e^{\frac{\pi}{2}i}\] and then raise it to the ith power

OpenStudy (anonymous):

arnab

OpenStudy (anonymous):

you get \[e^{-\frac{\pi}{2}}\]

OpenStudy (anonymous):

beautiful!

OpenStudy (anonymous):

thnx and only one cup of coffee

OpenStudy (anonymous):

cant get the probability question though

OpenStudy (anonymous):

Let i^i = e^x -> i ln i = x i ln (sqrt(-1)) = x i/2 ln -1 = x but since ln -1 = ipi x = -pi/2

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