Complex Numbers: Representations

This lecture aims to enhance intuition about complex numbers by representing them in various ways, simplifying calculations. Geometric representations of complex numbers are explored, where a complex number z = a + ib is viewed as a point in the plane. The Gauss representation identifies C with R², where z is represented as (a, b) in R². The module of a complex number |z| is the norm of the vector OM(z), and the trigonometric representation of a complex number is discussed using the exponential form cos(y) + i sin(y). The lecture also covers the Taylor polynomials for exponential functions, showing the remarkable synthesis between exponential and trigonometric functions.