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Further Pure Mathematics 1 (Edexcel) – Sample chapter

Chapters:
  FP1 (Edexcel): Chapter 1: Inequlaities Inequalities involving polynomial or rational functions, Inequalities involving the modulus function, Using algebraic and graphical methods
  FP1 (Edexcel): Chapter 2: Series Summation of finite series using standard results, Method of differences
  FP1 (Edexcel): Chapter 3: Complex numbers Adding, subtracting and multiplying complex numbers, Complex conjugates, Solutions of quadratic equations, Representing complex numbers geometrically, Modulus-argument form, Square roots of a complex number, Equating real and imaginary parts
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.
  • Be able to multiply and divide complex numbers given in modulus-argument form.
  • Understand the geometrical effects of multiplying and dividing two complex numbers.
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The Argand Diagram
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Multiplication in the Argand Diagram
Teach yourself
Polar form
Teach yourself
Multiplying and dividing in polar form
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
TestTest Questions
Submit answers Complex numbers 3
Complex numbers chapter assessment
This glossary covers all of this chapter.
Glossary
  FP1 (Edexcel): Chapter 4: Numerical solution of equations Interval bisection, Linear interpolation, The Newton-Raphson method
  FP1 (Edexcel): Chapter 5: First order differential equations Finding solutions of first order differential equations with separable variables, Sketching families of solution curves for first order differential equations with separable variables, Solving first order linear differential equations
  FP1 (Edexcel): Chapter 6: Second order differential equations Finding the general solutions of homogeneous second order differential equations with constant coefficients, Finding the general and particular solutions of non-homogeneous second order differential equations with constant coefficients
  FP1 (Edexcel): Chapter 7: Polar coordinates Converting from polar to cartesian coordinates and vice-versa, Sketching curves with simple polar equations, Finding the area enclosed by a polar curve, Finding tangents parallel to or perpendicular to the initial line