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Further Pure Mathematics 1 (Edexcel) – (2008 Spec)

Chapters:
  FP1 (Edexcel) (2008 spec): Chapter 1: Complex numbers Complex Numbers
Sections

Teachers' resources for complex numbers

Introduction to Complex Numbers

Before you start...
  • You need to be able to use the quadratic formula to solve quadratic equations.
When you have finished you should...
  • Be able to add, subtract, multiply and divide complex numbers.
  • Know what is meant by a complex conjugate.
  • Be able to find the solutions of any quadratic equation with real coefficients, and know that non-real roots occur in conjugate pairs.
Teach yourself
Addition and subtraction of complex numbers
Teach yourself
Multiplying complex numbers
Teach yourself
Dividing complex numbers
Teach yourself
Questions involving complex conjugates
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Working with Complex Numbers
Complex roots and the graph of a quadratic equation
Complex roots
TestTest Questions
Submit answers Complex numbers 1

The Argand diagram and the modulus-argument form

Before you start...
  • You need to have covered section 1.
  • You need to know the trigonometry work from C2, including radians, and the sine, cosine and tangent of angles greater than 90°. If you have not yet covered this work, there are some additional notes to help you.
When you have finished you should...
  • Represent complex numbers geometrically by means of an Argand diagram.
  • Understand the geometrical effects of conjugating a complex number and of adding and subtracting two complex numbers.
  • Understand the meanings of the modulus and argument of a complex number.
  • Be able to find the modulus and argument of a complex number.
  • Know that |z1z2| = |z1||z2|.
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The Argand Diagram
Teach yourself
Polar form
This is a puzzle to test your manipulation skills of complex numbers. Either do it yourself or, better, work with a partner or in a small group.
Complex Numbers puzzle
TestTest Questions
Submit answers Complex numbers 2

Complex numbers and equations

Before you start...
  • You need to have covered sections 1 and 2.
  • You need to be able to use the quadratic formula to solve quadratic equations.
  • You should be familiar with the factor theorem.
  • You need to be able to divide a cubic or quartic expression by a linear or quadratic factor.
  • You need to be able to solve a pair of simultaneous equations.
When you have finished you should...
  • Know that non-real roots of any polynomial equation with real coefficients occur in conjugate pairs.
  • Be able to find the two square roots of a complex number.
  • Be able to solve equations involving complex numbers by comparing real and imaginary parts.
Complex roots and the graph of a quadratic equation
Complex roots
Factorising cubics
Factorising quartics
TestTest Questions
Submit answers Complex numbers 3
Complex numbers chapter assessment
This glossary covers all of this chapter.
Glossary
  FP1 (Edexcel) (2008 Spec): Chapter 2: Numerical Methods Numerical Methods
  FP1 (Edexcel) (2008 Spec): Chapter 3: Coordinate systems Coordinate systems
  FP1 (Edexcel) (2008 Spec): Chapter 4: Matrices Matrices
  FP1 (Edexcel) (2008 Spec): Chapter 5: Series and Induction Series and Induction