Complex Numbers: Lecture Notes, Exercises, and Argand Diagrams

This document provides a comprehensive set of lecture notes on complex numbers, covering fundamental concepts and advanced topics. The notes begin with the definition of complex numbers, their real and imaginary parts, and the concept of equality. It then delves into the arithmetic of complex numbers, including addition, subtraction, scalar multiplication, multiplication, and division, along with examples. The concept of the complex conjugate is introduced, and its properties are discussed. The notes then transition to the geometrical representation of complex numbers on the Argand diagram, the polar form of a complex number, including modulus and argument, and how to convert between Cartesian and polar forms. Several exercises are provided throughout the notes to reinforce understanding and application of the concepts. The document also includes examples and detailed explanations, making it a valuable resource for students studying complex numbers. This document is available on Desklib, a platform providing past papers and solved assignments for students.