i-i-

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

i^{i} = ?

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

i = e^{\frac{i π}{2}} \Rightarrow i^{i} = {(e^{\frac{i π}{2}})}^{i} = e^{\frac{- π}{2}}

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

i^{2} = e^{i π}

i = e^{\frac{i π}{2}}

i^{i} = e^{\frac{i^{2} π}{2}} = e^{\frac{- π}{2}}

O r

i^{i} = y

i l o g i = l o g y

i . \frac{i π}{2} = l o g y

y = e^{- \frac{π}{2}}