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Edexcel A-Level Mathematics AS Fp1 1 3 Argand Diagrams and Complex Operations Questions

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

Edexcel A-Level Mathematics AS Fp1 1 3 Argand Diagrams and Complex Operations Questions 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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