Quote by Simon Bridge
Oh right.
You were thinking that k can be any complex not a negative real?
Positive reals can have real squareroots fersure, but I don't see how excluding negative reals from k helps considering you are allowing any complex number otherwise.
Normally the radical indicates a positive square root so that if ##y=x^2## then ##x\in\{\pm\sqrt{y}\}## ... that can mess things up. The result is that the negative reals are excluded, by definition, from the solution set.
This what you are thinking of?

Not quite (and my apologies for the confusion), this isn't an attempt to define where √k is true but to show where a specific identity is true.
In other words if you want to see √3 as a function of '3' and 'phi' then this function will give an exact result but it does not work for √3≠f(3,phi), although it will for √(3)^(1/2)=f((3)^(1/2),phi). Does that clear things up?
Quote by Simon Bridge
Don't know what you mean by "general form function" in this context.
Anyway  that would be for another thread ;)

I can't think of an example off the the of my head but, as you say, a discussion for another thread.