Question Number 100585 by Rio Michael last updated on 27/Jun/20
$$\:\mathrm{Given}\:\mathrm{that}\:\:{G}\:=\:\left\{\mathrm{1},\left({x}\:+\:{yi}\right),\left({x}−{yi}\right)\right\}\:\mathrm{form}\:\mathrm{a}\:\mathrm{group} \\ $$$$\mathrm{under}\:\mathrm{complex}\:\mathrm{multiplication},\:\mathrm{describe}\:\mathrm{the}\:\mathrm{locus} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{point}\:\left({x},{y}\right) \\ $$