2025 RVHS P2 Q2

The points \(A\), \(B\) and \(C\) represent the complex numbers \(z_A = 5 + 6\mathrm{i}\), \(z_B = 9 + 3\mathrm{i}\) and \(z_C\) respectively. \(ABC\) is an isosceles triangle labelled in a clockwise direction where \(\angle CAB = 90{}^\circ\).

1. Find \(z_C\).[3]
2. The point \(D\) representing the complex number \(z_D\), is such that \(ABDC\) is a parallelogram. Find \(z_D\).[2]