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Further Pure Mathematics 1 (OCR) – Sample chapter

Chapters:
  FP1 (OCR): Matrices Operations of matrices, Inverse matrices, Products of inverse matrices, Transformations, Matrices and simultaneous equations
  FP1 (OCR): Complex numbers The growth of the number system, Working with complex numbers, Representing complex numbers geometrically, Sets of points in an Argand diagram, The modulus-argument form of complex numbers, Sets of points using the modulus-argument form, Complex numbers and equations
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.
  • Be able to solve equations involving complex numbers by comparing real and imaginary parts.
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

Equations and geometrical representation

Before you start...
  • You need to have covered section 1.
  • 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.
  • 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.
  • 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.
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The Argand Diagram
TestTest Questions
Submit answers Complex numbers 2

Modulus-Argument Form

Before you start...
  • You need to have covered sections 1 and 2.
  • 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...
  • Understand the meanings of the modulus and argument of a complex number.
  • Be able to find the modulus and argument of a complex number.
  • Be able to illustrate simple equations and inequalities involving. complex numbers by means of loci in an Argand diagram.
Spreadsheet to investigate loci
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Flash investigation of loci
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The Argand Diagram
Teach yourself
Polar form
TestTest Questions
Submit answers Complex numbers 3
Complex numbers chapter assessment
This glossary covers all of this chapter.
Glossary
  FP1 (OCR): Series and induction Summation of finite series using standard results, Method of differences, Convergence and sum to infinity, Proof by induction
  FP1 (MEI): Roots of polynomial equations Properties of the roots of polynomial equations, Finding equations with given roots