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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
1 year, 4 months 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.

- 1 year, 3 months ago