SCHOLAR :

1 Complex numbers 1.1 Complex numbers 1.2 Revision exercise Revision exercise 1.3 Introduction 1.4 Complex numbers and the complex plane Exercise on finding real and imaginary points Exercise on identifying points in the complex plane 1.5 The arithmetic of complex numbers 1.5.1 Addition and subtraction of complex numbers Exercise on adding complex numbers Interactive adding of two complex numbers Exercise on subtracting complex numbers Interactive subtraction of complex numbers 1.5.2 Multiplication of complex numbers Exercise on multiplying two complex numbers Exercise on finding the square roots of a complex number Interactive multiplication Interactive multiplication by i 1.5.3 Conjugates of complex numbers Interactive plotting of conjugates Exercise on finding conjugates of complex numbers 1.5.4 Division of complex numbers Exercise on dividing complex numbers. Interactive division Interactive division of complex numbers by i 1.6 The modulus, argument and polar form of a complex number Exercise in finding the modulus and argument Further exercise in finding the modulus and argument 1.7 Geometric interpretations Geometric activity Interactive triangle inequality Exercise on geometric interpretation 1.8 Fundamental theorem of algebra 1.9 Solving equations Solving complex equations exercise 1.10 De Moivre's theorem 1.10.1 Multiplication using polar form 1.10.2 De Moivre's theorem Exercise using De Moivre's theorem Further exercise on using De Moivre's theorem 1.10.3 De Moivre's theorem and multiple angle formulae 1.10.4 De Moivre's theorem and nth roots Interactive finding roots of unity Extension activities 1.11 Conjugate properties Exercise on conjugate properties. 1.12 Proofs 1.13 Summary 1.14 Extended information 1.15 Review exercise Review exercise 1.16 Advanced review exercise Advanced review exercise. 1.17 Set review exercise Set review exercise Glossary

©Heriot-Watt University 2001