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.

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

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.

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.

Is the exponent defined by a function?

Edited December 7, 200817 yr by Petanquell

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