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.