Course: Complex Analysis and Differential Equations

Complex Analysis

Complex numbers

  • Representation of complex numbers: coordinate form, polar form

  • Power and roots: De Moivre’s formula

    \begin{equation} (\mathrm{cos}\theta+i\mathrm{sin}\theta)^{n}=\mathrm{cos}\ n\theta+i\mathrm{sin}\ n\theta\nonumber \\ \end{equation}
Write each number in standard form
Compute the root.

Complex functions

Analytic functions

(a) Definitions