Do complex conjugates commute?

Question

I wasn't sure how to ask this question, but I was wondering whether (this came up in the context of quantum mechanics) the integral $$\int f_m ^* f_ndx=\int f_n ^* f_mdx$$ is in general true. I have a hazy idea from somewhere that it is but can't recall for sure. I know the information will be out there online, but I don't know what to search for. Many thanks.

Answer 1

For complex numbers $a,b$, we have $(a^*b)^* = ab^* = b^*a$. Consequently, we have $$ \int f_m ^* f_ndx=\int (f_n ^* f_m)^* dx =\left(\int f_n ^* f_mdx\right)^*. $$