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## Main Question or Discussion Point

I have a question about complex valued functions, say f(z) where z=x+iy is a complex variable.

Can every such complex valued function be represented by:

f(z)=u(x,y)+iv(x,y)?

Also, is the limit of the conjugate such a function equal to the conjugate of the limit of the function?

Something like:

lim[conjugate[f]] (?)= conjugate[lim[f]]

Can every such complex valued function be represented by:

f(z)=u(x,y)+iv(x,y)?

Also, is the limit of the conjugate such a function equal to the conjugate of the limit of the function?

Something like:

lim[conjugate[f]] (?)= conjugate[lim[f]]