I have encountered the following problem in one of my textbooks but I'm not really getting anywhere:
Let $f$ be complex-valued and piecewise continuous on the interval $[-\pi,\pi]$. Find the complex fourier series of $Re(f)$ on the basis of the complex Fourier series of $f$.
i.e we're given that $f$ has the complex Fourier coefficient $c_n$ and we want to express $Re(f)$'s fourier coefficients, $C_n$, in terms of $c_n$. Did i interpret this correct?
I've tried splitting $f=g+ih$ but i'm not managing to express $C_n$ in terms of known objects.
Thanks in advance.