Robert Gerbicz on Fri, 27 Jun 2008 02:44:02 +0200

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complex powers


It's interesting that Pari gives a concrete value for example I^I, because it has got infinite many values:
log(I)=1/2*Pi*I+2*k*Pi*I and using this I^I=exp(I*(Pi/2*I+2*k*Pi*I))=exp(-Pi*(1/2+2*k))
where k is an integer.

The major computer algebra softwares, Maple and Mathematica returns by the input if I type I^I
this should be done by Pari-Gp also. But it's interesting that both of them gives 0 for I^I-I^I, what is wrong.