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Pearson Edexcel IAL Mathematics FP1.1.3 Argand diagrams & complex operations

Practise placing complex roots on Argand diagrams, using conjugate symmetry and coordinates to find areas, perimeters and products.

Syllabus
First assessment 2019
Course
Mathematics YMA01
Level
AS

Exam points

  • plot conjugate roots and real roots on one Argand diagram with correct quadrants and scale
  • use distances between Argand points to calculate triangle areas or quadrilateral perimeters
  • interpret sums, products or quotients of complex numbers through positions on the diagram

FP1.1.3 - Argand diagrams and complex operations question 1

[Maximum number: 2]

In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.

f(z)=4z3+pz2−24z+108\mathrm{f}(z)=4 z^{3}+p z^{2}-24 z+108

where p is a constant.
Given that -3 is a root of the equation f(z)=0

show the roots of f(z)=0 on a single Argand diagram.

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