Question 5 - A-Level Maths

Given that \(z _ { 1 } = - 3 - 4 \mathrm { i }\) and \(z _ { 2 } = 4 - 3 \mathrm { i }\)
1. show, on an Argand diagram, the point \(P\) representing \(z _ { 1 }\) and the point \(Q\) representing \(z _ { 2 }\)
2. Given that \(O\) is the origin, show that \(O P\) is perpendicular to \(O Q\).
3. Show the point \(R\) on your diagram, where \(R\) represents \(z _ { 1 } + z _ { 2 }\)
4. Prove that \(O P R Q\) is a square.