1. The problem statement, all variables and given/known data I'm sorry in advance but this will contain a lot of words to describe the soluton as I"m not good with Latex. z_=conjugate Show that f(z) = z^2 * z_ is not holomorphic in C. At which points is it complex-differentiable? I think I solved the problem I"m just looking for a second view.(or multiples). 2. Relevant equations Cauchy–Riemann equations 3. The attempt at a solution Ok first I wrote f(z)=z*z*z_=z*|z^2|=(x+yi)(x^2+y^2) Using the first Cauchy–Riemann equation and calculating the partial diff with respect to x of the real part then calculating the partial diff with respect to y for the imaginary part I get: 2x^2+y^2=3yi+ix^2,this is not holomorphic but is complex diff at x=y=0. Is this correct?If not what should I do.(if you can provide answer with examples,or at least detailed, that with be great) Thank you.