Glossary

Revision and useful background
1 Polynomial equations
Expanding three brackets
Solving using the quadratic formula
Roots of equations and use of the discriminant
2 Circles
3 Trigonometry
Trigonometric functions
Radians
Exact values for trigonometric functions: special triangles
Another way of viewing trigonometric functions
Putting it together

Groups of numbers

Surds
Rules for surds
Simplifying expressions containing surds
Rationalising and more simplifying of expressions containing
surds
Equations involving surds

Polynomials
Completing the square
Long division
Factor and remainder theorems
1 The factor theorem
2 The remainder theorem

Complex numbers
Imaginary numbers
Manipulation of imaginary numbers
Complex numbers — the basics
Complex numbers and Argand diagrams
Manipulation of complex numbers
Addition and subtraction
Multiplication
Division
Mixing it up
The modulus
Polynomials again
The fundamental theorem of algebra
Quadratics
Cubics
Polar coordinates
Conversion from Cartesian form to polar form
Conversion from polar form to Cartesian form
Conversion using a calculator
Multiplying and dividing complex numbers in polar form
Mixing it up
Powers of complex numbers in polar form: de Moivre’s theorem
Solving polynomial equations using de Moivre’s theorem
Finding the locus of complex numbers subject to restrictions
1 Where the real and/or imaginary part of the complex number is restricted
2 Where the modulus of the complex number is restricted
3 Where the argument of the complex number is restricted

Practice tasks

Answers