We consider two signal $h(t)$ and $g(t)$ such that $$\int_{-\infty}^\infty |g(t)|^2dt<+\infty$$ $$\int_{-\infty}^\infty |f(t)|^2dt<+\infty$$ Parseval's theorem states that: $$\int_{-\infty}^\infty{h(t)g(t)^*dt}=\int_{-\infty}^\infty{H(\omega)G(\omega)^*d\omega}$$ where $^*$ is the conjugate and $H(\omega),G(\omega)$ are the Fourier Transforms.
This result is also valid if, instead of the integrals, there are the series and instead of the transforms there are the Fourier series?
You question follows from properties of the complex numbers. I'm assuming you're used to $j=\sqrt{-1}$ instead of $i=\sqrt{-1}$; so that's what I'll use. Let $z$ and $w$ be complex numbers. Then $$ z w^{\star} = \frac{1}{4}\sum_{n=0}^{3}j^{n}|z+j^{n}w|^{2} $$