[tangentspace]

I always liked how Feynman dealt with complex numbers in 'QED: The Strange Theory of Light and Matter'.

He focuses on the intuitive concept of a particle having a spinny arrow attached, the arrow rotates as the particle flies through space. He only casually mentions that this is in fact a complex number, whereas the bulk of the text focuses on developing intuition around arrows.

I read that book in high school, and it certainly influenced the direction I took in university. It helped to understand that the physical universe often appears to behave in extremely non-intuitive ways, but using mathematics we can develop a model that transforms the phenomenon into something that actually does make intuitive sense.

I think some of the harder concepts in math are difficult because they act like stepping stones into aspects of our world that just don't make sense based on day-to-day experiences. But modern technology depends on this! Pedagogy is improving, but it still lags advances in technology.