
Re: What's the geometry meaning of i^i ?
Posted:
Jul 26, 2012 8:18 AM


Am 26.07.2012 07:09 schrieb Hongyi Zhao: > On Thu, 26 Jul 2012 05:21:56 +0200, Gottfried Helms wrote: > >> ... using rectangular coordinates and interpret them as polar ones (in >> principle)? > > What do you mean, could you please give some more detail explanations? > > Regards > Hmm. Assume z0 = a + b*i where i is the imaginary unit. Then consider z1 = e^z0 = exp(z0) = e^a * e^(bi) and e^a defines the length and e^(bi) the arc of the vectorial representation of z1. Assume then new letters for the rectangular coordinaters of z1: z1 = A + B*i Then consider the iteration z2 = e^z1 = e^A * e^(Bi) So the exponentiation can be understood as reintrpretation of the rectangular coordinates as coordinates in a polar representation.
Using i instead of e as basis for the exponentiation adds a bit of complication, since i = e^(Pi/2*i), but that complication is not so weird...
Gottfried

