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Recurring powers of iota

What is the value of \(\huge i^{i^{i^{i^{\cdot^{\cdot^\cdot}}}}} \)?

Clarification: \(i=\sqrt{-1}\).

Note by Mohit Bhalla
10 months, 2 weeks ago

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Hint: The expression be equal to \(a+ib\) for some . Then, \(a+ib=i^{(a+ib)}\implies a=e^(-\pi b/2)\cos(a\pi /2), b=e^(−\pi b/2)\sin(a\pi /2)\implies a^2+b^2=e^{-\pi b},\ b=a\tan (a\pi /2)\). One needs to solve the resulting set of transcendental equations. Samrat Mukhopadhyay · 9 months, 3 weeks ago

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