[ajross]

It's actually not more "complicated" in the sense of operation count. You divide in the standard algorithm by: shifting your divisor so it's within one bit of the dividend (or one "place" if you're doing non-binary math), subtracting (or doing a one-digit divide for human numbers), and then shifting the result left by one place and repeating until you're out of divisor.

Multiplication is completely symmetric: shift off the lowest bit (digit), multiply (which is just logical AND for binary), add to the result, shift the result right, and repeat.

The reason multiplication is faster than division isn't about complexity it's about dependency. The division steps depend on the previous iteration, where multiplication can be parallelized.