bob000555 Posted November 27, 2008 Posted November 27, 2008 What is i to the power of infinity? As near as I can figure either the answer is the matrix [-1, 1, i , -i], or 0.
Shadow Posted November 27, 2008 Posted November 27, 2008 I believe it's "undefined + undefined i" ) That's what Maple gave me anyway. I could tell you what an infinite power tower made out of i's is, but that's about it. Cheers, Gabe
Bignose Posted November 27, 2008 Posted November 27, 2008 It's just another of math's undefined terms, like 0/0 or infinity/infinity. In general these have no meaning, though sometimes they can point out where problems are.
Xanadu Posted December 1, 2008 Posted December 1, 2008 The way to approach this is to turn i^infinity into a limit. i^infinity is the same as the limit as n goes to infinity of i^n. Since this limit doesn't converge, it doesn't exist, and so i^infinity is undefined. 1
Petanquell Posted December 7, 2008 Posted December 7, 2008 (edited) Is the exponent defined by a function? Edited December 7, 2008 by Petanquell
Twerpy Posted December 10, 2008 Posted December 10, 2008 What is i to the power of infinity? As near as I can figure either the answer is the matrix [-1, 1, i , -i], or 0. It's undefined. You're assuming that infinity acts as a real number. It doesn't. Is the exponent defined by a function? It's defined by an infinite power series
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