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Re:A Visual, Intuitive Guide to Imaginary Numbers (2007) by kevin_thibedeau on Friday August 10, 2018 @06:21PM (#17737126)
They are only really useful in the science and engineering fields that need them. That is why they remain opaque to most people. High school level pedagogy doesn't deal effectively with the useful applications of these concepts (matrices are also poorly introduced).

Most of our modern technology would not be achievable without the use of complex numbers as a tool.

Re:A Visual, Intuitive Guide to Imaginary Numbers (2007) by tangentspace on Friday August 10, 2018 @08:35PM (#17737643)
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.