Electrical engineer here, which is 90% dealing with imaginary numbers. On that comment on using pairs of real numbers instead of imaginary numbers:

My uncle had (and gave me) a very old book on electrical engineering that described all of the equations and theory without ever mentioning imaginary numbers - they used vectors instead, so they had to tap into vector calculations for even the most basic operations.

Needless to say I never really read it as it was borderline impossible to follow once you knew how easy it would be to do the same with imaginary numbers instead...

edit. typos...