The differentiability of the complex valued function $(Rez)(Imz)z\over|z|^2$

Question

$$ f(z) = \left\{ \begin{array}{ll} \Re(z)\Im(z)z\over|z|^2 & \quad z \neq 0 \\ 0 & \quad z = 0 \end{array} \right. $$ I want to prove that this function is not complex differentiable at 0 but not sure what sort of an approach should be taken. Hope someone could assist me on this. Thanks