Re: i to the ith power
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Re: i to the ith power
The book I mentioned here yesterday is "An Imaginary tale: The Story of
sqrt(-1)" by Paul J. Nahin [Princeton University Press, 1998]. Perhaps not
quite as immediately readable as the nice books on the history of math by Eli
Maior (The Story of e; Trigonometric Delights), but there is a great deal in
the book that would be accessible to any intelligent reader.
The author specifically deals with the question of computing i^i in Appendix C,
as well as dealing with this sort of thing more generally in the main text
(tracing such computations back to Euler). The basic idea is to notice that
e^(i*pi) is -1, so that the square root of this, or i, is e^(i*pi/2).
Then, using the laws of exponents, we get i^i = e^(-pi/2), a real number!
Is the TI-83 this clever when you feed in i^i? I doubt it! Is the TI-89 this
clever? Maybe, maybe...
RWW Taylor
National Technical Institute for the Deaf
Rochester Institute of Technology
Rochester NY 14623
>>>> The plural of mongoose begins with p. <<<<
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