We are asked to prove $ f = z^{3}e^{1-z} = 1 $ has exactly 2 roots inside $|z| = 1$
We've tried creating functions $p$ and $q$ where $p + q = f$, $p$ with 2 roots inside our boundary, and using Rouche's Thm, but we keep on getting equality. I feel like we're missing something. Any hints or direction is greatly appreciated. Thanks in advance.