Imaginary numbers have always intrigued me from the very beginning I was taught to believe that some negative root number could have an "i" factored out!(adsbygoogle = window.adsbygoogle || []).push({});

Anyway, I like to know more about this identity if anyone can help me out:

(1+i)^(1+i) = e^ln(root 2)-pi(1/4+2k)e^i(ln(root2)+pi(1/4+2k))

I'm not quite sure as to how 1+i = root 2e^(pi/4+2pi k). I do know that i^i = e^-pi/2 from the identity e^ipi=-1 which gives i = ln(-1)/pi. So my question is why is 1+i = root 2e^(pi/4+2pi k) true? This statement does not seem to make sense to me because it describes both cosine and sine giving 1 as an answer which does not seem to be the case on the unit circle and neither from Euler's identity

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# Exotic imaginaries

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