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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 $i^x = x$. – Strin Jun 17 '12 at 03:54
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1It's possible that it doesn't even converge, so that trick may not work, Strin. – Potato Jun 17 '12 at 03:58
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4Well, what branch shall you choose? – Pedro Jun 17 '12 at 04:12
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This blog article on Walking Randomly is related but does not answer your specific question: http://www.walkingrandomly.com/?p=294 – tomcuchta Jun 17 '12 at 04:16
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Smells like $W$. – anon Jun 17 '12 at 04:18
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3This question seems on the same subject. – DSM Jun 17 '12 at 04:21