In case of complex numbers what is the value of $i^i$

Asked Oct 02 '17 at 14:03

Active Oct 18 '17 at 16:22

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Is it possible to get the value of $i^i$? I want to know what the result of it is.

edited Oct 18 '17 at 16:22

Michael Rozenberg

194,933

asked Oct 02 '17 at 14:03

Abdullah Al Naeem

1

Even Google knows. – Zubzub Oct 02 '17 at 14:07

1 Answers1

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$$i^i=\left(e^{\frac{i\pi}{2}+2i\pi k}\right)^i,$$ where $k\in\mathbb Z$.

I think it's clear now.

edited Oct 02 '17 at 14:17

answered Oct 02 '17 at 14:06

Michael Rozenberg

194,933

I would add $=e^{-\frac\pi2+2k\pi i}$. – José Carlos Santos Oct 02 '17 at 14:09
@ José Carlos Santos Yes of course! – Michael Rozenberg Oct 02 '17 at 14:13