9709 P32 - Mar 2021 - Q8 - 9 marks
10442
The complex numbers u and v are defined by u=−4+2i and v=3+i.
(a) Find u/v in the form x+iy, where x and y are real. [3]
(b) Hence express u/v in the form \(re^{i\theta}\), where r and θ are exact. [2]
In an Argand diagram, with origin O, the points A, B and C represent the complex numbers u, v and 2u+v respectively.
(c) State fully the geometrical relationship between OA and BC. [2]
(d) Prove that angle AOB=3π/4. [2]
