I've been trying to show that $\displaystyle 1/1-z^4 $ is analytic (whenever it's defined) using the Cauchy-Riemann equations. But I get some pretty ugly expressions that I can't simplify if I use $\displaystyle z = x + iy$ or polar form. Is there some way around it, or should I stick with that method and the expressions will simplify once I partially differentiate?

Thanks for any help!