## Complex Numbers Made SimpleComplex Numbers lie at the heart of most technical and scientific subjects. This book can be used to teach complex numbers as a course text,a revision or remedial guide, or as a self-teaching work. The author has designed the book to be a flexible learning tool, suitable for A-Level students as well as other students in higher and further education whose courses include a substantial maths component (e.g. BTEC or GNVQ science and engineering courses). Verity Carr has accumulated nearly thirty years of experience teaching mathematics at all levels and has a rare gift for making mathematics simple and enjoyable. At Brooklands College, she has taken a leading role in the development of a highly successful Mathematics Workshop. This series of Made Simple Maths books widens her audience but continues to provide the kind of straightforward and logical approach she has developed over her years of teaching. |

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### Contents

Chapter 1 The quadratic formula | 1 |

Chapter 2 The algebra of complex numbers | 7 |

Chapter 3 The Argand diagram | 17 |

Chapter 4 The modulus argument form for a complex number | 19 |

Chapter 5 Products and quotients using the rcosθ +isinθ form | 31 |

Chapter 6 The four operations on the Argand diagram | 39 |

Chapter 7 Useful facts | 45 |

Chapter 8 A sample question | 47 |

Chapter 12 Use of De Moivres theorem II | 67 |

Chapter 13 The cube roots of unity | 71 |

Chapter 14 The nth roots of unity where n is a positive integer | 77 |

Chapter 15 The nth roots of any complex number | 81 |

Chapter 16 The exponential form for a complex number | 89 |

Chapter 17 Locus questions plural is loci | 95 |

Chapter 18 Transformations of the Argand diagram | 111 |

Chapter 19 A sample question | 119 |

Chapter 9 Further questions | 49 |

Chapter 10 De Moivres theorem | 57 |

Chapter 11 Use of De Moivres theorem I | 63 |

Chapter 20 Further questions | 123 |

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1st quadrant 2abi airl algebra arctan arg z2 arg(z Argand diagram aró Binomial theorem Brooklands College Cartesian equation Chapter circle centre common eenee complex conjugates complex number cos2kt cosé diagram by point distance between x,y eubatituting eubtending example Exercise 1.1 factor find the image Find the modulus find the roots find the values form r(cos formula giving your answers Hence find i.ein iein imaginary axis imaginary numbers integral valuee isin least value Level locus of Q London modulus and argument Moivre's theorem multiplied nth roots Pageplus part-line Pascal's triangle point P(x,y point representing point x,y positive integer principal value prove Pure Maths quadratic equation question r,6 form radians radius real number real roote representing the complex rhombue roots of unity sketch the locus square roots thie three roots vector Verity x-axis z-plane z1 and z2