/sci/ - Science & Math

It simplifies loads of real (badum tss) problems and this is all because of
>>3137608

this is the one in important property of field of complexes, namely that it includes the real numbers but is algebraically closed
http://en.wikipedia.org/wiki/Algebraically_closed_field
specifically it fulfills
http://en.wikipedia.org/wiki/Fundamental_theorem_of_algebra

tl;dr: if you have a polynomial eqation, say
x^7-2x^3+1=0
then you know that there are 7 solutions.

The equation x^2+6=0 just over the reals has no solutions

what would you say is more essential to quantum mechanics (including QFT ect.)
the superposition principle or the definition of observables?
or something else?
and what is so special about the superposition principle and about the definition of observables

So mathematica 8 is out.
From peoples who use mathematica: Hopes? Expectations? ..