Find the value of i^i ?


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Question Number 27603 by lizan 123 last updated on 10/Jan/18

$F i n d t h e v a l u e o f i^{i} ?$
Commented by abdo imad last updated on 10/Jan/18

$i f y o u m e a n i / i^{2} = - 1 w e h a v e i^{i} = e^{i l n (i)}$ $a n d l n (i) m e a n t h e p r i c i p a l d e t e r m i n a t i o n o f c o m p l e x$ $l o g a r i t h m e b u t i = e^{i \frac{π}{2}} \Rightarrow l n (i) = \frac{i π}{2} \Rightarrow e^{i l n (i)} = e^{- \frac{π}{2}}$ $i^{i} = e^{- \frac{π}{2}} .$
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