To be quite frank, you’re avoiding complex numbers only in the sense that you spell out the operations involved in handling complex numbers explicitly—so of course there’s no added benefit, you’re simply lifting the lid of the box...
That being said, as you discover by decomposing complex multiplication into it’s parts (rotation and scaling), you get to play with them separately, which already leads you to discover interesting new variations on the theme.
To be quite frank, you’re avoiding complex numbers only in the sense that you spell out the operations involved in handling complex numbers explicitly—so of course there’s no added benefit, you’re simply lifting the lid of the box...
That being said, as you discover by decomposing complex multiplication into it’s parts (rotation and scaling), you get to play with them separately, which already leads you to discover interesting new variations on the theme.