Toppers Notes on The Complex Numbers

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Table of Content

  • Definition of complex numbers.
  • Algebraic operations with complex numbers.
  • Geometrical representation of complex numbers.
  • Conjugate of complex numbers.
  • Properties of the conjugate of complex numbers.
  • Modulus of the complex numbers.
  • Properties of the modulus of the complex numbers.
  • The polar form of the complex numbers.
  • The Eular form of the complex numbers (Exponential form of the complex numbers).
  • The argument of the complex numbers.
  • Properties of the argument of the complex numbers.
  • Vector representation of the complex numbers.
  • Rotation theorem for the complex numbers.
  • Application of the complex numbers in co-ordinate geometry.
  • Representation of some loci of the complex numbers.
  • The square root of a complex number.
  • De Moiver’s theorem and its application.
  • The nth root of unity.
  • Complex cube root of unity.
  • The nth root of a complex number.
  • Rational power of a complex number.
  • The logarithm of a complex number.