Somebody can give me a hand with this?

Given the unitary operator $U=1+i\varepsilon F$ (where $\varepsilon$ is an infinitesimal escalar), in order to prove that $F$ is Hermitean:

$$UU^{+}=1$$

$$(1+i\varepsilon F) (1-i\varepsilon F^+)=1$$

$$1+i\varepsilon F-i\varepsilon F^+ +\varepsilon^2 FF^+=1$$

It seems that $F$ must be equal to $F^+$ to satisfy that expression, but how can the remaining term be equal to zero? $(\varepsilon^2 FF^+\overset{\large\text{?}} = 0)$

Given the unitary operator $U=1+i\varepsilon F$ (where $\varepsilon$ is an infinitesimal scalar), in order to prove that $F$ is Hermitian:

$$\begin{align} UU^{\dagger} &= 1 \\ (1+i\varepsilon F) (1-i\varepsilon F^\dagger) &= 1 \\ 1+i\varepsilon F-i\varepsilon F^\dagger +\varepsilon^2 FF^\dagger &= 1 \end{align}$$

It seems that $F$ must be equal to $F^\dagger$ to satisfy that expression, but how can the remaining term be equal to zero? $(\varepsilon^2 FF^\dagger\overset{\large\text{?}} = 0)$