Cauchy Riemann Equations for $h(z)=|z|^2z^2$ A past exam question I have come across is...
Is the following function differentiable on $\mathbb{C}$
$h(z)=|z|^2z^2$
I have calculated $u(x,y)=x^4-y^4$ and $v(x,y)=2x^3y+2xy^3$
I then have
$\frac{du}{dx}=4x^3,$ 
$\frac{dv}{dx}=6x^2y+2y^3$
$ \frac{dv}{dy}=-4y^3$
$ \frac{dv}{dy}=2x^3+6xy^2$
hence these do not satisfy the Cauchy Riemann equations as $\frac{du}{dx} \neq\frac{dv}{dy}, -\frac{dv}{dx} \neq \frac{du}{dy}$
Is this enough to show that its not differentiable on $\mathbb{C}$??

Yes.  Analytic functions must satisfy the Cauchy Riemann equations.  These do not.
