Question Number 221393 by universe last updated on 02/Jun/25
$$\:\:\:\:\:{a},\:{b},\:{c}\:{are}\:{complex}\:{number}\:{and}\: \\ $$$$\:\:\:\mid{a}\mid\:=\:\mid{b}\mid=\mid{c}\mid=\:\mathrm{1}\:{and}\:\:\frac{{a}^{\mathrm{2}} }{{bc}}+\frac{{b}^{\mathrm{2}} }{{ac}}\:+\frac{{c}^{\mathrm{2}} }{{ab}}\:=\:−\mathrm{1} \\ $$$$\:\:\:\:{where}\:\mid.\mid\:{is}\:\:{modules}\:{function} \\ $$$${then}\:\mid{a}+{b}+{c}\mid\:{can}\:{be}\: \\ $$$$\left({A}\right)\:\mathrm{0}\:\:\:\:\:\:\:\left({B}\right)\:\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\left({C}\right)\:\frac{\mathrm{3}}{\mathrm{2}}\:\:\:\:\:\:\:\:\:\:\left({D}\right)\:\mathrm{2} \\ $$