How does one interpret the correlation between a real function, x[n], and a complex exponential, $$e^{-j\omega n}$$, where j represents the imaginary part. Follows a well known example:
$$\chi\left(\omega\right)=\sum _{n=-\infty }^{\infty }\:x\left[n\right]e^{-j\omega n}$$
I guess I found the intuition I was looking for. In this case, the correlation is a complex number, and it is higher the farther away from the origin it is. The multiplication of these two functions can be viewed as a "2D object" whose samples summation is a kind of a center of mass.
The correlation between these two functions is higher when the center of mass is farther away from the center.
Reference: https://youtu.be/spUNpyF58BY?t=1088