I can't understand how to proceed with the example. I have to "find the equation of the equilevel lines at constant $u=u_0$ and constant $v=v_0$ of the function $e^z = u(x,y)+iv(x,y)$ and the equations of the lines which map $x=x_0$ and $y=y_0$ in the u-v plane."
I started with $e^z = e^{x+iy}=e^xe^{iy}$ and, as I understand, I have to get two functions $u(x,y)$ and $v(x,y)$, then set $x$ and $y$ to constant (for example in the class we were shown how for $f(z) = z^2$ we got $u(x,y)=x^2-y^2$ and $v(x,y) = 2xy$, fixing $x$ and $y$, forming two parabolas).
But if in case of $f(z) = z^2$ it was easy to find, here I just stuck with $e^xe^{iy}$ not knowing how can I separate it into $u$ and $v$