" 

 == Complex dot product and more general definition == 

 The definition of a dot product for complex vectors is more general, and i'm thinking it wouldn't be a bad idea to simply make that the main definition at the top. Most people learning about the dot product wouldn't be confused if a note about the complex conjugate were given ""for real numbers, the complex conjugate of a number is equal to that number, and so that operation may be ignored in the case of real numbers"". Comments?  "