Eisenstein integer

Definitions

A complex number of the form a+bω, where a and b are integers and ω is defined by the following two rules: (1) ω³=1 and (2) 1+ω+ω²=0; an element of the Euclidean domain ℤ[ω].

Examples

“To divide⟳ an Eisenstein integer a#43;b#92;omega by another Eisenstein integer c#43;d#92;omega, notice⟳ that (c#43;d#92;omega)(c#43;d)(c#43;d#92;omega²)#61;c³#43;d³; accordingly multiply⟳ both denominator and numerator (of the division expressed as a fraction) by (c#43;d)(c#43;d#92;omega²), then simplify⟳.”

CEFR level