Complex Dot Products

The main thing to understand here is that the complex dot product allows us to find to dot product of the real inputs, and imaginary inputs in a single computationcomputation.

As previously discussed, the output of the real dot product outputs a single real number indicating the correlation / strength of relationship between the 2 input vectors.

With complex dot products, the process and concepts are the same, its just that the output is a complex number.

However, the correlation exists as the magnitude of this output complex number. The practical effect is changes input phase do not impact the resultant correlation,  as we use both the real and imaginary component of the complex number to find the correlation and they end up evening out. However, if we were only doing real dot products (IE, only using the 'X' real axis / component of the input complex number), then our result would be affected by the phase.

This is important to understand for understanding Fourier Transformations

This part may be hard to fully grasp right now, but try your best to understand the above explanation and keep it in mind as we discuss the Fourier Transform