what is value of i to the power of i (iota)?

Asked by Bhavi Khatri | 9th Sep, 2015, 03:55: PM

Expert Answer:

F r o m space E u l e r apostrophe s space F o r m u l a comma space w e space k n o w space t h a t comma e to the power of i x end exponent equals cos x plus i sin x S i n c e space e to the power of iπ over 2 end exponent equals cos straight pi over 2 plus i sin straight pi over 2 rightwards double arrow space e to the power of fraction numerator i pi over denominator 2 end fraction end exponent equals i therefore i to the power of i equals open parentheses e to the power of fraction numerator i pi over denominator 2 end fraction end exponent close parentheses to the power of i rightwards double arrow i to the power of i equals open parentheses e to the power of fraction numerator i squared pi over denominator 2 end fraction end exponent close parentheses rightwards double arrow i to the power of i equals open parentheses e to the power of fraction numerator negative pi over denominator 2 end fraction end exponent close parentheses therefore i to the power of i equals e to the power of fraction numerator negative pi over denominator 2 end fraction end exponent

Answered by Vimala Ramamurthy | 9th Sep, 2015, 05:29: PM

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