Define $f: \mathbb{C} \rightarrow \mathbb{C}$ as
$f(z):= \begin{cases}\exp(-z^{-4}), &x \ne 0\\ 0, &x=0.\end{cases}$
Show that $F(x_1,x_2):=(\text{Re}(f(x_1+ix_2)),\text{Im}(f(x_1+ix_2)))$ satisfies the Cauchy-Riemann equations at all points in $\mathbb{R}^2$ but it's not complex differentiable
I think I have to expand the term $e^{(-(x+iy)^{-4})}$ to find the real and imaginary part of the function. But I'm having problems trying to do so. Any help would be really appreciated.