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Question Number 109005 by Study last updated on 20/Aug/20

$$i^i=?$$

Answered by floor(10²Eta[1]) last updated on 20/Aug/20

$$\mathrm{i}={\mathrm{e}}^{\frac{\mathrm{i}\pi }{2}}\Rightarrow {\mathrm{i}}^{\mathrm{i}}={\left({\mathrm{e}}^{\frac{\mathrm{i}\pi }{2}}\right)}^{\mathrm{i}}={\mathrm{e}}^{\frac{-\pi }{2}}$$

Answered by Dwaipayan Shikari last updated on 20/Aug/20

$$i^2=e^{i\pi }$$$$i=e^{\frac{i\pi }{2}}$$$$i^i=e^{\frac{i^2\pi }{2}}=e^{\frac{-\pi }{2}}$$$$Or$$$$i^i=y$$$$ilogi=logy$$$$i.\frac{i\pi }{2}=logy$$$$y=e^{-\frac{\pi }{2}}$$

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