Q$3)(30$ points$)$ Let

$f(z)=\{\begin{array}{ccc}\frac{?}{\text{b}\text{a}\text{r}}& (z{)}^3,& z0\\ z^2,& z=0\\ 0,& z=0\end{array}$

Show that

$($a$)f(z)$ is continuous everywhere on $C.$

$($b$)f^{\text{'}}(0)$ does not exist, that is$,f(z)$ is not differentiable at the point $z=0.$

Q$4)(30$ points$)$ Determine at which points the function

$f(z)=x^3+i($:$1-y$:${)}^3$

differentiable, and write $f^{\text{'}}(z)$ at those points.