CAIE P3 2020 Specimen — Question 6

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2020
SessionSpecimen
TopicComplex Numbers Arithmetic
TypeMulti-part questions with division as one step

6 Th cm plexm b rs \(1 + B\) ad \(4 + \quad 2\) are \(d \mathbf { b }\) ed \(\forall u\) ad \(v\) resp ctie ly.
  1. Fid \(\frac { \mathrm { u } } { \mathrm { V } }\) irt b fo \(\mathrm { m } x + \mathrm { i } y , \mathrm { w } \mathbf { b }\) re \(x\) ad \(y\) are real.
  2. State th argn en \(6 \frac { u } { v }\). In an Arg nd id ag am, with o ign \(O\), th \(\dot { \mathrm { p } } \mathrm { ns } A , B\) ad \(C\) represen th cm p ex m b rs \(u , v\) ad \(u - v\) resp ctie ly.
  3. State fullyt bg m etrical relatio h申 tween \(O C\) ad \(B A\).
  4. Sth the tag e \(A O B = \frac { 1 } { 4 } \pi\) rad as.