OCR MEI Further Pure Core AS 2022 June — Question 7

Exam BoardOCR MEI
ModuleFurther Pure Core AS (Further Pure Core AS)
Year2022
SessionJune
TopicComplex Numbers Argand & Loci

7 On an Argand diagram, the point A represents the complex number \(z\) with modulus 2 and argument \(\frac { 1 } { 3 } \pi\). The point B represents \(\frac { 1 } { z }\).
  1. Sketch an Argand diagram showing the origin O and the points A and B .
  2. The point C is such that OACB is a parallelogram. C represents the complex number \(w\). Determine each of the following.
    • The modulus of \(w\), giving your answer in exact form.
    • The argument of \(w\), giving your answer correct to \(\mathbf { 3 }\) significant figures.