Complex numbers

Introduction to complex numbers
Algebraic form, real part, imaginary part, modulus, conjugate, triangular inequality
Sum, product and inverse
Calculations, 2nd-degree equation with complex coefficients
Plane representation, affix of a point
Work with multiplication by the conjugate in the case of fractions of two polynomials to obtain the algebraic form of the quotient, Exponential form, link with geometry (modulus, argument)
Euler and Moivre, use complexes to linearize cos^n(x), sin^n(x) and to express cos(px), sin(px) using powers
nth roots with special case of square roots