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 $(x,y)\mapsto (x+x^2-y^2,2xy-y)$ ?