SCHOLAR
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Contents - 1 Complex numbers
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
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Assessment, test or quiz
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Heriot-Watt University 2001