Why does FFT output need to conjugate processing?
The real part represents cosine correlation, and the imaginary coefficient represent the sine correlation.  Cosines are even or symmetric functions in the DFT aperture, and sines are odd functions (or anti-symmetric) in the DFT aperture.  So you can only ignore the imaginary coefficients for exactly symmetric input.

Conjugation and multiplication is “just” a mathematical trick (identity) to compute sin^2 + cos^2 which is the hypotenuse squared (Pythagoras).