I have some information but i do not know whether it is true or not .
the complex numbers used in
calculating the spread of germs
in census of population
in complex integrals
in engineering
in laser disks CD and hard disks industry ( in equation uncountable part with real number so we use imaginary part and if we reduce imaginary part the disk capacity will increase )
in signal processing ( have effective role in telephone technology , wireless connection ... etc
I would say that all numbers,words and images are an abstraction of our minds. see "ceci n'est pas une pipe." https://en.wikipedia.org/wiki/The_Treachery_of_Images . However, we have defined these to have direct relevance to certain real physical measurements. I have struggled with complex numbers and have determined this: Preprint Quantum wave function realism, time, and the imaginary unit i