complex system, three variables and equations
Source: VJIMC 2002 2.1
July 17, 2021
algebracomplex numberssystem of equations
Problem Statement
Find all complex solutions to the system
\begin{align*}
(a+ic)^3+(ia+b)^3+(-b+ic)^3&=-6,\\
(a+ic)^2+(ia+b)^2+(-b+ic)^2&=6,\\
(1+i)a+2ic&=0.\end{align*}