Question

На множестве комплексных чисел решить уравнение:
8i-z³=0

Answer 1

$z=a+bi=>z^3=a^3+3a^2bi-3ab^2-b^3i=(a^3-3ab^2)+i(3a^2b-b^3)\\ (a^3-3ab^2)+i(3a^2b-b^3)=8i=>\left \{ {{a^3-3ab^2=0} \atop {3a^2b-b^3=8}} \right. =>\left \{ {{a(a^2-3b^2)=0} \atop {3a^2b-b^3=8}} \right.\\ (1)\;a=0=>-b^3=8=>b=-2\\ (2)\;a^2=3b^2=>3*3b^2*b-b^3=8=>b^3=1=>b=1=>a^2=3=>a=\pm\sqrt3\\ \fbox{OTBET:}\;\; z=-2i, z=\pm\sqrt3+i$