I may be showing my ignorance, but I believe brushless DC motors run on three phase AC. Why is it called a DC motor?
Well... Brushless DC motors run on batteries when you put them in an electric car, and 3-phase AC induction motors do the same. That's not the part that makes classifies them as AC or DC electric motors.
Wikipedia's opinion: "...more a de facto convention rather than a rigid distinction."
Brushless DC (BLDC) motors DO look and act a lot like 3-phase AC induction motors - including needing a more complicated controller than a series wound DC motor - but the torque curve of a BLDC motor is more similar to a permanent magnet DC motor (because that's basically what it is), and induction (slip) doesn't generate torque as it does in a 3-phase AC induction motor.