Name: Dunny P.
I am having a hard time trying to figure out how to raise
the imaginary unit i to the imaginary power i.
In other words: i^i = ?
Where can I find more information on complex forms of Ln?
Raising complex numbers to powers is often simplified by using Euler's
exp(i*x) = cos(x) +i*sin(x)
You see for example, that for x=pi this becomes exp(i*pi) = -1 since
Similarly, exp(i * pi/2) = i, since cos(pi/2) = 0 and sin(pi/2) = 1
So i^i = [exp(i*pi/2)]^i = exp(i^2 *pi/2) = exp(-1*pi/2) = 0.207879...
WHICH IS REAL! AMAZING these complex numbers!
I think you will have to consult a textbook on complex variables to get
detailed info on
log functions of complex numbers, and of trig functions.
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Update: June 2012