I am trying to find how many zeros of the given function f are located in the unit disk $|z|<1$:
$f(z) = e^z - 4z^n + 1$, where $n=1,2,3,...$
Using Rouche's Theorem, which states that if both $f$ and $g$ are holomorphic inside and on some closed contour $C$, and $|f(z)| > |g(z)|$ for all $z \in C$, then $f$ and $f+g$ have the same number of zeros inside of $C$. I started by letting $f(z) = -4z^n+1$ and $g(z) = e^z$. My problem is how to figure the answer out using Rouche's Theorem.