For any complex inner product space, for two arbitrary elements $x,y$, we have the following relationship:
$$ \langle x,y \rangle = \frac{1}{2 \pi} \int_0^{2 \pi} \| x + e^{it}y \|^2 e^{it} dt $$
This is straight forward to prove but I am wondering how to interpret this result, or how to think about it intuitively.