Tower of imaginary units

Algebra Level 3

Compute the value of ( ( ( i i ) i ) i ) ⋯ ) i ⏟ 1001 i ’s \underbrace{ (((i^i)^i)^i)^\cdots )^i }_{\text{1001 }i\text{'s}} for i = − 1 i = \sqrt{-1} .

i i i^{i} − 1 -1 i i − i -i

Ekesh Kumar by Ekesh Kumar , 20, USA

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1 solution

Ekesh Kumar
Aug 24, 2017

Rewrite as ( ( i i ) 2010 ) ((i^{i})^{2010}) which gives i 1 = i i^{1} = i

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