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A 2D or x-y coordinate function has a complex analog, which is formed by replacing x with with the complex variable z. That function can then be separated into real and imaginary parts. Graphing the real part, produces a 3D graph with the vertical slice along the x-axis corresponding to the original 2D function. However, it doesn't seem impossible that another real component of a complex function somewhere may in fact reduce to this same original 2D function. Is it possible to know if there are other such functions? If yes, is there a method of searching for such a function?

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User3910
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  • Is your original function a map $\mathbb R\rightarrow\mathbb R$? It isn't clear what you mean. Can you furnish an example of the "original" and the "complexified" function? – MPW Jan 22 '15 at 22:24
  • @MPW I believe the answer is yes, for more info see the link in my question. – User3910 Jan 22 '15 at 22:26

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