derivatives of complex functions (x^3+3xy^2-3x)+i(y^3+3x^2y-3y)

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You're doing some complex analysis there, doesn't seem like a precalc problem.  However, if you use the Cauchy-Schwartz theorem you should find that the second equation doesn't hold.  The partial of the first equation with respect to y does not equal negative the partial of the second equation with respect to x.  I did it quickly in my head, but I don't believe that this function is analytic.