2022 NJC P1 Q4

Two complex numbers \(w\) and \(u\) satisfy the equations

\({{w}^{*}}-2\mathbf{i}u=8\) and \((2\mathbf{i}-1)w+2{{u}^{*}}=4\).

Find \(w\) and \(u\), giving your answers in the form \(x+\mathbf{i}y\), where \(x\) and \(y\) are real.[4]

Given that both \(w\) and \(u\) are roots of the equation \(\left( {{z}^{2}}-4z+c \right)\left( {{z}^{2}}-dz+10 \right)=0\), find the values of the real numbers \(c\) and \(d\).[3]