[cushychicken]

You're right that complex numbers simplify the math incredibly. Being able to move everything to the baseband is a huge help.

I think the fundamental problem is that:

1) there isn't a whole lot of comfort with complex numbers generally, so getting rid of them makes the material seem more approachable - at the cost of being significantly more complicated, and

2) a lack of good resources for implementing common DSP algorithms in actual hardware. The jump from Matlab to raw C is mystifying to many people (myself included in many cases).

I actually prefer Lyons's Understanding Digital Signal Processing as an intro text over this one.

I also really benefitted from having a good teacher in this stuff. Dan Boschen with DSPrelated runs some great online classes on DSP that helped me immensely in understanding this material. About $200 for five classes, with tons of great iPython notebooks of examples. (He was the one who helped me get the "all math works the same at baseband" advantage of complex numbers.)

[teleforce]

Based on the current trend the wireless modulation eco-system is moving towards time-frequency-spatial-polarization for better capacity and reliability. Not unlike the 3D graphics/multimedia eco-system sooner or later quaternion math will soon be a common thing, and textbook need to be re-written, expanded and updated due to complex number's limitations.