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Value of iⁱ

MediumCalculus~6m

The imaginary unit raised to itself, iii^i, is a real number. What is its value? (to 3 decimals)

Show hints (2)+
  1. Write ii as eiπ/2e^{i\pi/2}.
  2. (eiπ/2)i=e−π/2(e^{i\pi/2})^i = e^{-\pi/2}.

Answer

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0.2079 (± 0.005)

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Asked at: Jane Street

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