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How to compute the infinite tower of the complex number $i$, that is$ ^{\infty}i$

Define $a_0 = i$, and $a_n = i^{a_{n-1}}$.

What is

$$\lim_{n \rightarrow \infty}{a_n} = i^{i^{\,{}^{.\,^{.\,^{.\,^i}}}}} = ~~~? $$

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    This is equivalent to the solution of $i^x = x$.2012-06-17
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    It's possible that it doesn't even converge, so that trick may not work, Strin.2012-06-17
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    Well, what branch shall you choose?2012-06-17
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    This blog article on Walking Randomly is related but does not answer your specific question: http://www.walkingrandomly.com/?p=2942012-06-17
  • 0
    Smells like $W$.2012-06-17
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    [This question](http://math.stackexchange.com/questions/17578/how-to-compute-the-infinite-tower-of-the-complex-number-i-that-is-inftyi) seems on the same subject.2012-06-17

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