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This question is from a math-essentials booklet for physicists. The function is not analytic from the C-R conditions but that is all I know.

$ \rlap{\textbf{-------------------------------------------------------------------------------------------------}}{\mbox{Its derivative should be}}$ $2z + 2\bar{z} =4Re[z]$ So are its critical points all over the real axis?

The question also asks for a roiugh sketch of the graph. How would I sketch $(x,y)\mapsto (x+x^2-y^2,2xy-y)$ ?

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    What do you mean by its derivative? $\bar{z}$ is not complex differentiable.2011-03-17
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    @Alex I thought critical values were where the derivative of the function goes to zero i.e extremal and inflection points. I would correct the mistake, though I am even more lost now.2011-03-17
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    @Approximist: That's the definition for real functions and I believe for holomorphic complex functions as well. In this context, however, I have no idea what the definition would be.2011-03-17

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