Previously, I found $a \bmod b = a - b \left\lfloor \frac{a}{b} \right\rfloor$ and wondered if this could be extended to the complex plane. I did this, and it seems to yield interesting results, such as the fact that when it seems to form a dihedral group under addition. Is this already an area of study within mathematics? I tried looking it up, but whenever I do I get the modulus of a complex number instead.
2026-03-26 19:20:05.1774552805
Implications of Modular Arithmetic in the Complex Plane Defined as $z_1 \bmod z_2 = z_1 - z_2 \left\lfloor \frac{z_1}{z_2} \right\rfloor$?
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