SPS SPS FM Pure 2023 February — Question 11

Exam BoardSPS
ModuleSPS FM Pure (SPS FM Pure)
Year2023
SessionFebruary
TopicComplex Numbers Argand & Loci

11. In an Argand diagram, the points \(A , B\) and \(C\) are the vertices of an equilateral triangle with its centre at the origin. The point \(A\) represents the complex number \(6 + 2 \mathrm { i }\).
  1. Find the complex numbers represented by the points \(B\) and \(C\), giving your answers in the form \(x + \mathrm { i } y\), where \(x\) and \(y\) are real and exact. The points \(D , E\) and \(F\) are the midpoints of the sides of triangle \(A B C\).
  2. Find the exact area of triangle \(D E F\).
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