2025 TJC P1 Q8

The complex numbers \(z\) and \(w\) satisfy the following equations.

\(2z+\left| w \right|=2-4i\)

\(iz-w=2i\)

Find \(z\) and \(w\), giving your answers in the form \(a+ib\), where \(a\) and \(b\) are real numbers.[5]

It is given that \({{z}_{1}}=2-i\) and \({{z}_{3}}=-3+2i\). On an Argand diagram, mark the points \(A\) and \(C\) representing \({{z}_{1}}\) and \({{z}_{3}}\) respectively.[1]

The points \(B\) and \(D\) on the Argand diagram represent complex numbers \({{z}_{2}}\) and \({{z}_{4}}\) respectively. Given that \(ABCD\) is a square, labelled in an anti-clockwise direction, find \({{z}_{2}}\) and \({{z}_{4}}\).[4]