Socratus unlike others you have at least made efforts to read and understand.
So lets see if I can get you a bit futher along.
Lubos Motl did a really good article on why quantum mechanics
has to be complex and linear. It has some heavy mathematics
but the mathematics is not essential to the understanding.
Read around the mathematics and see if you can follow the
science logic of how and why QM works.
The last few paragraphs spell it out for you very neatly
and concisely.
http://motls.blogspot.com.au/2012/08/why-quantum-mechanics-has-to-be-complex.htmlFeel free to ask about anything you don't get.
The author of
http://motls.blogspot.com.au/2012/08/why-quantum-mechanics-has-to-be-complex.htmtry to explain:
Why real numbers aren't good enough in QT
(in Schrödinger's equation, Feynman's path integral,
and Heisenberg's uncertainty principle ) .
Why pure imaginary numbers are needed in QT
Why complex numbers are fundamental in physics .
This is another specific theme.
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P.S.
As regarding imaginary numbers I agree with G. Leibniz,
who wrote in 1702 that
‘ Imaginary numbers are beautiful and wonderful asylum
of divine spirit almost amphibian of genesis with non genesis’.
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