For complex numbers or quaternions, is there another two variable function, that behaves like addition? I mean a function f with(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

af(b,c)=f(ab,ac)

[/tex]

[tex]

f(a,b)=f(b,a)

[/tex]

[tex]

f(a,f(b,c))=f(f(a,b),c)

[/tex]

And which conditions have to be imposed to make this function uniquely [itex]f(a,b)=a+b[/itex]?

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# Alternative way to add numbers

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